Catalan Numbers with Applications

Catalan Numbers with Applications

Volumn , Issue , 2009, Pages 1-304

  Koshy, Thomas ^a  

^a FRAMINGHAM STATE UNIVERSITY   (United States)

Author keywords

Catalan numbers; Catalan sequence; Euler's triangulation problem; Fibonacci numbers; Lucas numbers; Martin gardner; Parenthesization problem; Pascal's identity; Pascal's triangle

Indexed keywords

EID: 77955203637     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780195334548.001.0001     Document Type: Book

References (355)

1. Abbott, H. L. Problem E 2799, American Mathematical Monthly 87 (Dec. 1980), 825.
2. Alagar, V. S. Fundamentals of Computing: Theory and Practice, Prentice-Hall, Englewood Cliffs, NJ, 1989, 621-622.
3. Alter, R. "Some Remarks and Results on Catalan Numbers," Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computing (1971) 109-132.
4. Alter, R., and K. K. Kubota. "Prime and Prime Power Divisiblity of Catalan Numbers," Notices of the AMS 19 (1972), A-48.
5. Alter, R., and K. K. Kubota. "Prime and Prime Power Divisiblity of Catalan Numbers," Journal of Combinatorial Theory, Series A, 15 (1973), 243-256.
6. Alter, R., and T. B. Curtz. "On Binary Nonassociative Products and Their Relation to a Classical Problem of Euler," Roczniki Polskiego Towarzystwa Mathematics 17 (1973), 1-8.
7. Andersen, E. Solution to Problem E 2083, American Mathematical Monthly 76 (April 1969), 419-420.
8. Andreoli, M. Problem 630, College Mathematics Journal 30 (May 1999), 234.
9. Ayers, F. Jr. Problem 3803, American Mathematical Monthly 43 (Nov. 1936), 580.
10. Bager, A. Solution to Problem E 2659, American Mathematical Monthly 85 (Nov. 1978), 767-768.
11. Bailey, D. F. "Counting Arrangements of 1s and -1s," Mathematics Magazine 69 (1996), 128-131.
12. Balakrishnan, V. K. Theory and Problems of Combinatorics, Schaum's Outline Series, McGraw-Hill, New York, 1995, 27-33.
13. Balakram, H. "On the Values of n Which Make (2n)!/(n+1)!(n+1)! an Integer," Journal of the Indian Mathematical Society 18 (Oct. 1929), 97-100.
14. Barlaz, J. Problem 4742, American Mathematical Monthly 54 (May 1957), 370.
15. Bassali, W. A. Letter to the Editor, Mathematics Magazine 62 (April 1989), 148.
16. Becker, H. W. "Rooks and Rhymes," Bulletin of the AMS 52 (1946), 1016.
17. Becker, H. W. "Books and Rhymes," Mathematics Magazine 22 (1948), 23-26.
18. Becker, H. W. Solution to Problem 4277, American Mathematical Monthly, 56 (Dec.1949), 697-698.
19. Becker, H. W. "The Closed Diagonal Binomial Coefficient Expansion," Bulletin of the AMS 57 (1951), 298.
20. Becker, H. W. "Planar Rhyme Schemes," Bulletin of the AMS 58 (1952), 39.
21. Beineke, L. W., and R. E. Pippert. "A Census of Ball and Disk Dissections," Lecture Notes in Mathematics (by A. Dold), Springer-Verlag, New York, 1964.
22. Beineke, L. W., and R. E. Pippert. "Enumerating Dissectible Polyhedra by Their Automorphism Groups," Canadian Journal of Mathematics 1 (1974), 50-67.
23. Berman, G., and K. D. Fryer. Introduction to Combinatorics, Academic Press, New York, 1972.
24. Bernstein, K. L. Solution to Problem 1213, Mathematics Magazine 59 (April 1986), 116-117.
25. Beumer, M. G. Solution to Problem E 2054, American Mathematical Monthly 76 (Feb. 1969), 193.
26. Beyler, R. H. <> Biasotti, J. et al. Solution to Problem 1213, Mathematics Magazine 59 (April 1986), 116.
27. Bird, M. T. Solution to Problem 5178, American Mathematical Monthly 73 (Feb. 1965), 203-204.
28. Birkhoff, G. Problem 3674, American Mathematical Monthly 41 (April 1934), 269.
29. Bivens, I. C., and B. G. Klein. Solution to Problem 1269, Mathematics Magazine 61 (June 1988), 200-201.
30. Bizley, M. T. L. Solution to Problem 5178, American Mathematical Monthly 72 (Feb. 1965), 203.
31. Blackwell, D., and J. L. Hodges Jr. "Elementary Path Counts," American Mathematical Monthly 74 (1967), 801-804.
32. Borwein, J. M., and P. B. Borwein. Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, Wiley, New York, 1987.
33. Boucher, C. L. "Path Representation of a Free Throw Shooter's Progress," Mathematics Magazine 79 (June 2006), 213-217.
34. Boyd, A. V. Problem E 2409, American Mathematical Monthly 80 (April 1973), 434.
35. Boyer, R. H. Problem 4510, American Mathematical Monthly 61 (Feb. 1954), 129.
36. Brawley, J. V. "Dedicated to Leonard Carlitz: The Man and His Work," Finite Fields and Their Applications 1 (1995), 135-151.
37. Brenner, J. L., and R. J. Evans. Letter to the Editor, Mathematics Magazine 61 (June 1988), 207.
38. Breusch, R. Problem 4742, American Mathematical Monthly 55 (April 1958), 293.
39. Breusch, R. Problem 5178, American Mathematical Monthly 71 (Feb. 1964), 217.
40. Bristol, W. A., and W. R. Church. Solution to Problem 3421, American Mathematical Monthly 38 (Jan. 1931), 54-55.
41. Brown, J. L., and V. E. Hoggatt Jr. "A Primer for the Fibonacci Numbers, Part XVI: The Central Column Sequence," Fibonacci Quarterly 16 (Feb. 1978), 41-46.
42. Brown, J. R. Solution to Problem 4931, American Mathematical Monthly 68 (Dec. 1961), 1012.
43. Brown, S. H. "An Interview with H. W. Gould," College Mathematics Journal, 37 (Nov. 2006), 370-379.
44. Brown, W. G. "Historical Note on a Recurrent Combinatorial Problem," American Mathematical Monthly 72 (1965), 973-977.
45. Bruckman, P. S. Problem H-616, Fibonacci Quarterly 42 (Nov. 2004), 377.
46. Bruckman, P. S. Problem 1134, Pi Mu Epsilon Journal 12 (Spring 2007), 365.
47. Callan, D. "Certificates of Integrality for Linear Binomials," Fibonacci Quarterly 38 (Aug. 2000), 317-325.
48. Callan, D. Problem 11091, American Mathematical Monthly 111 (June-July 2004), 534.
49. Campbell, D. M. "The Computation of Catalan Numbers," Mathematics Magazine 57 (Sept. 1984), 195-208.
50. Cantor, D. G. Problem 4764, American Mathematical Monthly 65 (Oct. 1958), 637.
51. Carlitz, L. Solution to Problem E 1854, American Mathematical Monthly 74 (May 1967), 596.
52. Carlitz, L. "Enumeration of Certain Sequences," Acta Arithmetica 18 (1971), 221-232.
53. Carlitz, L. "Sequences, Paths, Ballot Numbers," Fibonacci Quarterly 10 (Nov. 1972), 531-549.
54. Carlitz, L. Problem H-209, Fibonacci Quarterly 11 (Feb. 1973), 73.
55. Carlitz, L. Solution to Problem H-209, Fibonacci Quarterly 12 (Dec. 1974), 400.
56. Carlitz, L. et al, "Some Remarks on Ballot-Type Sequences of Positive Integers," Combinatorial Structures and Their Applications, Gordon and Breach, New York, 1970.
57. Carlitz, L. et al, "Some Remarks on Ballot-Type Sequences of Positive Integers," Journal of Combinatorial Theory, Series A, 11 (1971), 258-271.
58. Carlitz, L., and J. Riordan. "Two Element Lattice Permuation Numbers and Their q-Generalization," Duke Mathematical Journal 31 (1964), 371-388.
59. Carlitz, L., and D. P. Roselle. "Triangular Arrays Subject to MacMahon's Conditions," Fibonacci Quarterly 10 (Dec. 1972), 591-597, 658.
60. Carlitz, L., and R. A. Scoville, Problem E 2054, American Mathematical Monthly 75 (Jan. 1968), 77.
61. Carlitz, L., and R. A. Scoville. "A Generating Function for Triangular Partitions," Mathematics of Computation 29 (Jan. 1975), 67-77.
62. Carlitz, L., and R. A. Scoville. "Note on Weighted Sequences," Fibonacci Quarterly 13 (Dec. 1975), 303-306.
63. Castellanos, D. "The Ubiquitous π," Mathematics Magazine 61 (April 1988), 67-98, 148-163.
64. Cayley, A. "On the Partitions of a Polygon," Proceedings of the London Mathematical Society 22 (1891), 237-262.
65. Chamberlain, M. Solution to Problem 290, College Mathematics Journal 17 (Sept. 1986), 364-365.
66. Chandrasekharan, K. Introduction to Analytic Number Theory, Springer-Verlag, New York, 1968.
67. Chang, G. Problem 290, College Mathematics Journal 15 (Nov. 1984), 446.
68. Chapman, R. Solution to Problem 11165, American Mathematical Monthly 114 (May 2007), 454-455.
69. Chernoff, P. R. Solution to Problem E 1896, American Mathematical Monthly 74 (Oct. 1967), 1007.
70. Christophe, L. M. Jr. Problem 1269, Mathematics Magazine 60 (June 1987), 178.
71. Chu, W. "A New Combinatorial Interpretation for Generalized Catalan Number," Discrete Mathematics 65 (1987), 91-94.
72. Church, C. A. Jr. Solution to Problem 5343, American Mathematical Monthly 73 (Dec. 1966), 1129-1130.
73. Clarke, R. J. Letter to the Editor, Mathematics Magazine 61 (Oct. 1988), 269.
74. Cofman, J. "Catalan Numbers for the Classroom?," Elemente der Mathematik 52 (1997), 108-117.
75. Cohn. D. I. A. Basic Techniques of Combinatorial Theory, Wiley, New York, 1978.
76. Comtet, L. Advanced Combinatorics, Dreidel, Boston, Massachusetts, 1974.
77. Conway, J. H., and H. S. M. Coexter. "Triangulated Polygons and Frieze Patterns," Mathematical Gazette 57 (1973), 87-94; 175-183.
78. Conway, J. H., and R. K. Guy. The Book of Numbers, Copernicus, New York, 1996, 97-106.
79. Cook, R. "A Mathematical Centenary: J. J. Sylvester 1814-1897," Mathematical Spectrum 30 (1997-1998), 1-2.
80. Corey, S. A. Problem 270, American Mathematical Monthly 16 (Jan. 1909), 40.
81. Corey, S. A. Solution to Problem 270, American Mathematical Monthly 17 (June-July 1909), 121.
82. Currier, A. E. Problem 4764, American Mathematical Monthly 64 (Dec. 1957), 737.
83. Dean, R. A., and Keller, G. "Natural Partial Orders," Canadian Journal of Mathematics 20 (1968), 535-554.
84. de Bruijn, N. G. and Morselt, B. J. M. "A Note on Plane Trees," Journal of Combinatorial Theory 2 (1967), 27-34.
85. Debus, A. G. (ed.)World Who's Who in Science, Marquis-Who's Who, Chicago, Illinois.
86. Deutsch, E. "An Involution on Dyck Paths and its Consequences," Discrete Mathematics, 204 (1999), 163-166.
87. Deutsch, E. Problem 11071, American Mathematical Monthly 111 (March 2004), 259.
88. Deutsch, E. Problem 11150, American Mathematical Monthly 112 (April 2005), 367.
89. Deutsch, E. Problem 11170, American Mathematical Monthly 112 (Aug.-Sept. 2005), 655.
90. Deutsch, E. Problem 1739, Mathematics Magazine 79 (Feb. 2006), 67-68.
91. Deutsch, E., and I. M. Gessel. Problem 1494, Mathematics Magazine 69 (April 1996), 143.
92. Deutsch, E., and W. P. Johnson. "Create Your Own Permutation Statistics," Mathematics Magazine 77 (April 2004), 130-134.
93. Deustch, E., and B. E. Sagan. "Congruences for Catalan and Motzkin Numbers and Related Sequences," Journal of Number Theory, 117 (2006), 191-215.
94. de Vries, H. L. "On Property B and on Steiner Systems," Mathematische Zeitschrift 153 (1977), 155-159.
95. Došlić, T. "Perfect Matchings, Catalan Numbers, and Pascal's Triangle," Mathematics Magazine 80 (June 2007), 219-226.
96. Dunkel, O. Problem 3421, American Mathematical Monthly 38 (1930), 196.
97. Dvoretzky, A., and T. Motzkin. "A Problem of Arrangements," Duke Mathematical Journal 14 (1947), 305-313.
98. Dymàček, W. M., and H. Sharp. Introduction to Discrete Mathematics, W. C. Brown/McGraw-Hill, Boston, Massachusetts, 1998.
99. Eggleton, R. B., and R. K. Guy. "Catalan Strikes Again! How Likely Is a Function to be Convex?," Mathematics Magazine 61 (Oct. 1988), 211-219.
100. Eldredge, G. Problem E 1903, American Mathematical Monthly 73 (1966), 666.
101. Elsner, C. "On Recurrence Formulae for Sums Involving Binomial Coefficients," Fibonacci Quarterly 43 (Feb. 2005), 31-45.
102. Eğecioğlu, O. "The Parity of the Catalan Numbers via Lattice Paths," Fibonacci Quarterly, 21 (Feb. 1983), 65-66.
103. Erdös, P. Problem 4252, American Mathematical Monthly 54 (May 1947), 287.
104. Erdös, P. "On Some Divisibility Properties of 2n/n ," Canadian Mathematics Bulletin 7 (1964), 513-518.
105. Erdöl;s, P. et al. "On the Prime Factors of 2n/n ," Mathematics of Computation 29 (Jan. 1975), 83-92.
106. Erdös, P., and I. Kaplansky. "Sequences of Plus and Minus," Scripta and Mathematics 12 (1946), 73-75.
107. Etherington, I. M. H. "Non-Associate Powers and a Functional Equation," Mathematical Gazette 21 (1937), 36-39, 153.
108. Etherington, I. M. H. "On Non-Associative Combinations," Proceedings of the Royal Society of Edinburgh 59 (1939), 153-162.
109. Etherington, I. M. H. "Some Problems of Nonassociative Combinations," Edinburgh Mathematical Notes 32 (1940), 1-6.
110. Even, S. Graph Algorithms, Computer Science Press, Rockville, Maryland, 1979.
111. Fechter,M.A. Solution to Problem E 1896,American Mathematical Monthly 74 (Oct. 1967), 1007-1008.
112. Feemster, H. C. Problem 172, American Mathematical Monthly 17 (March 1910), 75.
113. Feemster, H. C. Problem 175, American Mathematical Monthly 17 (June-July 1910), 150.
114. Feldman, H. M. Solution to Problem 230, American Mathematical Monthly 29 (Nov.-Dec. 1955), 109.
115. Feller, W. An Introduction to Probability Theory and Its Applications, vol. 1, Wiley, New York, 1957, 66-73.
116. Fine, N. J. "Binomial Coefficients Modulo a Prime," American Mathematical Monthly 54 (1947), 589-592.
117. Finkel, B. F. (ed.). Problem 2, American Mathematical Monthly 1 (Feb. 1894), 50.
118. Forder, H. G. "Some Problems in Combinatorics," Mathematical Gazette 45 (1961), 199-201.
119. Fraliegh, J. B. A First Course in Abstract Algebra, 7th ed., Addison-Wesley, Reading, Massachusetts, 2004.">Fraliegh, J. B. A First Course in Abstract Algebra, 7th ed., Addison-Wesley, Reading, Massachusetts, 2004.
120. Frame, J. S. Problem 5113, American Mathematical Monthly 70 (June-July 1963), 672.
121. Franklin, P. Problem 2681, American Mathematical Monthly 25 (March 1918), 118.
122. Fray, R. D. Solution to Problem E 2253, American Mathematical Monthly 78 (Sept. 1971), 797.
123. Fray, R. D., and D. P. Roselle. "Weighted Lattice paths," Pacific Journal of Mathematics 37 (1971), 85-96.
124. Fryer, W. D. Solution to Problem E 1700, American Mathematical Monthly 72 (May 1965), 553.
125. Gardner, M. "Mathematical Games," Scientific American 215 (Dec. 1966), 131.
126. Gardner, M. "Catalan Numbers: An Integer Sequence that Materializes in Unexpected Places," Scientific American 234 (June 1976), 120-125.
127. Gandhi, J. M. Problem E 1346, American Mathematical 66 (Jan. 1959), 61.
128. Gandhi, J. M. Problem E 5343, American Mathematical Monthly 72 (Dec. 1965), 1135.
129. GCHQ Problem Solving Group. Solution to Problem 11091, American Mathematical Monthly 113 (May 2006), 462-463.
130. Gehami, L. A. Problem E 2253, American Mathematical Monthly 77 (Oct. 1970), 882.
131. Gillispie, C. C. (ed.). Dictionary of Scientific Biography, Charles Scribner's Sons, NewYork, 1973.
132. Goheen, C. C. Problem 4931, American Mathematical Monthly 67 (Nov. 1960), 926.
133. Goldstone, L. D. Solution to Problem E 1346, American Mathematical Monthly 66 (Sept. 1959), 591.
134. Gould, H. W. Solution to Problem 676, American Mathematical Monthly 41 (May-June 1968), 166.
135. Gould, H.W. "Equal Products of Generalized Binomial Coefficeints," Fibonacci Quarterly 9 (Oct. 1971), 337-346.
136. Gould, H.W. "Fibonomial Catalan Numbers: Arithmetic Properties and a Table of the First Fifty Numbers," Notices of the AMS 18 (1971), 938.
137. Gould, H.W. "A New Primality Criterion of Mann and Shanks and its Relation to a Theorem of Hermite," Fibonacci Quarterly 10 (1972), 355-364, 372.
138. Gould, H.W. "Generalization of a Formula of Touchard for Catalan Numbers," Journal of Combinatorial Theory, Series A, 23 (1977), 351-353.
139. Gould, H. W. Bell and Catalan Numbers: Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown,West Verginia, 1978.
140. Graham, R. L. et al. Concrete Mathematics, 2nd ed., Addison-Wesley, Reading, Massachusetts, 1994.
141. Griffiths, R. L. "Catch-up Numbers," Mathematical Gazette 91 (Nov. 2007), 500-509.
142. Grimaldi, R. P. "The Catalan Numbers," MAA Minicourse, Orlando, Florida (Jan. 1996).
143. Grimaldi, R. P. Discrete and Combinatorial Mathematics, 5th ed., Pearson/Addison-Wesley, 2004.
144. Grossman, H. D. "Fun with Lattice Points," Scripta Mathematica 12 (1946), 223-225.
145. Grossman, H. D. "More about Lattice-Paths," Scripta Mathematica 14 (1948), 160-162.
146. Grossman, H. D. "Fun with Lattice Points," Scripta Mathematica 15 (1949), 79-81.
147. Grossman, H. D. "Fun with Lattice Points," Scripta Mathematica 16 (1950), 207-212.
148. Grosswald, E. Solution to Problem 6019, American Mathematical Monthly 84 (Jan. 1977), 63-65.
149. Growney, J. A. S. Finitely Generated Free Groups, Ph.D. dissertation, University of Oklahoma, Norman, 1970.
150. Gummer, C. F. Solution to Problem 2681, American Mathematical Monthly 27 (March 1919), 128.
151. Gupta, H. "On a Problem in Parity," Indian Journal of Mathematics 11 (1969), 157-163.
152. Gupta, H. "On the Parity of (n+m-1)(n,n)/n!m! ," Research Bulletin, Punjab University 20 (1969), 571-575.
153. Gupta, H. "Meanings of Non-Associative Expressions," Research Bulletin, Punjab University 21 (1970), 225-226.
154. Guy, R. K. "Dissecting a Polygon into Triangles," Research Paper no.9, Department of Mathematics, University of Calgary, Alberta, Canada (Jan. 1967).
155. Guy, R.K. "Dissecting a Polygon into Triangles," Bulletin of Malayan Mathematical Society 5 (1968), 57-60.
156. Guy, R. K. "A Medley of Malayan Mathematical Memories and Mantissae," Mathematical Medley 12 (1984), 9-17.
157. Guy, R. K. Letter to the Editor, Mathematics Magazine 61 (Oct. 1988), 269.
158. Guy, R. K. "The Second Strong Law of Small Numbers," Mathematics Magazine 63 (Feb 1990), 3-20.
159. Guy, R. K. "Parker's Permutation Problem Involves the Catalan Numbers," American Mathematical Monthly 100 (March 1993), 287-289.
160. Guy, R. K., and J. L. Selfridge. "The Nesting and Roosting Habits of the Laddered Parenthesis," Research Paper no. 127, Department of Mathematics, University of Calgary, Alberta, Canada (June 1971).
161. Guy, R. K., and J. L. Selfridge. "The Nesting and Roosting Habits of the Laddered Parenthesis," American Mathematical Monthly 80 (Oct. 1973), 868-876.
162. Handelsman, M. B. Problem 436, College Mathematics Journal 21 (Nov. 1990), ">Handelsman, M. B. Problem 436, College Mathematics Journal 21 (Nov. 1990), 423.
163. Harary, F. Applied Combinatorial Mathematics, Wiley, New York, 1964.
164. Harary, F. et al. "The Number of Plane Trees," Indagationes Mathematicae 26 (1964), 319-329.
165. Hayes, D. R. "Leonard Carlitz (1907-1999)," Notices of the AMS 48 (Dec. 2001), 1322-1323.
166. Herzog, F. Solution to Problem 4252, American Mathematical Monthly 56 (Jan. 1949), 42-43.
167. Heuer, G.A. Solution to Problem E 2054, American Mathematical Monthly 76 (Feb. 1969), 192-193.
168. Hilton, P., and J. J. Pedersen. Letter to the Editor, Mathematics Magazine 61 (June 1988), 207.
169. Hilton, P., and J. Pedersen. "The Ballot Problem and Catalan Numbers," Nieuw Archief Voor Wiskunde 7-8 (1990), 209-216.
170. Hilton, P., and J. Pedersen. "Catalan Numbers, Their Generalizations, and Their Uses," Mathematics Intelligencer 13 (1991), 64-75.
171. Hodges, J. H. Solution to Problem E 1346, American Mathematical Monthly 66 (Sept. 1959), 590.
172. Hoggatt, V. E. Jr., and M. Bicknell. "Pascal, Catalan, and General Sequence Convolution Arrays in a Matrix," Fibonacci Quarterly 14 (1976), 135-143.
173. Hoggatt, V. E. Jr., and M. Bicknell. "Catalan and Related Sequences Arising from Inverses of Pascal's Triangle Matrices," Fibonacci Quarterly 14 (Oct. 1976), 395-405.
174. Hoggatt, V. E. Jr., and M. Bicknell. "Sequences of Matrix Inverses from Pascal, Catalan, and Related Convolution Arrays," Fibonacci Quarterly 14 (Dec. 1976), 224-232.
175. Hoggatt, V. E. Jr., and M. Bicknell. "Numerator Polynomial Coefficient Arrays for Catalan and Related Sequence Convolution Triangles," Fibonacci Quarterly 15 (1977), 30-34.
176. Holshouser, A. L. Problem E 2659, American Mathematical Monthly 84 (June-July 1977), 486.
177. Howard, F. T. "In Memoriam-Leonard Carlitz," Fibonacci Quarterly 38 (Aug. 2000), 316.
178. Howard, H. R. Problem 2714, American Mathematical Monthly 25 (June 1918), 259.
179. Howard, H. R. Solution to Problem 2714, American Mathematical Monthly 26 (Sept. 1919), 318.
180. Howell, J. M. Problem 230, Mathematics Magazine 28 (March 1955), 233.
181. Hsu, L. C. Problem E 995, American Mathematical Monthly 58 (Dec. 1951), 700.
182. Huff, G. B. Problem E 2520, American Mathematical Monthly 82 (Feb. 1975), 169.
183. Irwin, F. Problem 2688, American Mathematical Monthly 25 (March 1918), 119.
184. Irwin, F. Solution to Problem 2688, American Mathematical Monthly 33 (Feb. 1926), 105.
185. Jackson, D. E., and R. C. Entringer. "Enumeration of Certain Binary Matrices," Journal of Combinatorial Theory 8 (1970), 291-298.
186. Jarvis, F. "Catalan Numbers," Mathematical Spectrum 36 (2003-2004), 9-12.
187. Just, E. Problem E 2083, American Mathematical Monthly 75 (April 1968), 404.
188. Kapur, J. N. "Combinatorial Analysis and School Mathematics," Educational Studies in Mathematics 3 (1970), 111-127.
189. Kelly, J. B. Solution to Problem 4983, American Mathematical Monthly 69 (Nov. 1962), 931.
190. Kemeny, J. G., and J. L. Snell. "A Combinatorial Formula," Mathematical Models in the Social Sciences, MIT Press, Cambridge, Massachusetts, 1975.
191. Kim, K. H., and F.W. Roush. "Enumeration of Semiorders and Transitive Relations," Notices of the AMS 24 (1977), 1-10.
192. King, J., and P. King. Solution to Problem 87.F, Mathematical Gazette 90 (March 2006), 163-164.
193. Klambauer, G. Problems and Propositions in Analysis, Marcel Dekker, NewYork, 1979.
194. Klamkin, M. S. Problem 4983, American Mathematical Monthly 68 (Oct. 1961), 807.
195. Klamkin, M. S. Problem 488, College Mathematics Journal 23 (Nov. 1992), 435-436.
196. Klarner, D.A. "A Correspondence between Two Sets of Trees," Indagationes Mathematicae 31 (1969), 292-296.
197. Klarner, D. A. "Correspondence between Plane Trees and Binary Sequences," Journal of Combinatorial Theory 9 (1970), 401-411.
198. Klazar,M. "On abab-Free and abba-Free Set Partitions," European Journal of Mathematics 1 (1996), 53-68.
199. Klazar, M. "Counting Even and Odd Partitions," American Mathematical Monthly 110 (June-July 2003), 527-531.
200. Knott, G. D. "A Numbering System for Binary Trees," Communications of the ACM 20 (Feb. 1977), 113-115.
201. Koehler, J. E. "Folding a Strip of Stamps," Journal of Combinatorial Theory 5 (1968), 135-152.
202. Koshy, T. Fibonacci and Lucas Numbers with Applications, Wiley, NewYork, 2001.
203. Koshy, T. Discrete Mathematics with Applications, Elsevier/Academic Press, Boston, Massachusets, 2004.
204. Koshy, T. "The Ubiquitous Catalan Numbers," Mathematics Teacher 100 (Oct. 2006), 184-188.
205. Koshy, T. Elementary Number Theory with Applications, 2nd ed., Academic Press, Burlington, Massachusetts, 2007.
206. Koshy, T., and M. Salmassi. "Parity and Primality of Catalan Numbers," College Mathematics Journal 37 (Jan, 2006), 52-53.
207. Kotlarski, I. I. Solution to Problem E 2409, American Mathematical Monthly 81 (April 1974), 408-409.
208. Krier, N. K., and F. R. Bernhart. Problem 1213, Mathematics Magazine 58 (March 1985), 111.
209. Kruse, R. L. Data Structures and Program Design, 2nd ed., Prentice Hall, Englewood cliffs, New Jersey, 1987.
210. Kuchinski, M. J. "Catalan Structures and Correspondences," Master's thesis, West Virginia University, Morgantown,West Virginia, 1977.
211. Lafer, P., and Long, C. T. "A Combinatorial Problem," American Mathematical Monthly 69 (Nov. 1962), 876-883.
212. Larcombe, P. J. "On Pre-Catalan Catalan Numbers:Kotelnikow(1766)," Mathematics Today, 35 (Feb. 1999), 25.
213. Larcombe, P. J. "On the History of the Catalan Numbers: A First Record in China," Mathematics Today 35 (June 1999), 89.
214. Larcombe, P. J. "The 18th Century Chinese Discovery of the Catalan Numbers," Mathematical Spectrum 32 (Nov. 1999), 5-7.
215. Larcombe, P. J., and P. D. C.Wilson. "On the Trail of the Catalan Sequence," Mathematics Today 34 (Aug. 1998), 114-117.
216. Lass, H. Solution to Problem E 2174. American Mathematical Monthly 77 (Feb. 1970), 195-196.
217. Lehmer, D. H. Solution to Problem E 760, American Mathematical Monthly 54 (Oct. 1947), 478.
218. Lehmer, D. H. "Interesting Series Involving the Central Binomial Coefficients," American Mathematical Monthly 92 (Aug.-Sept. 1985), 449-457.
219. Lehmer, E. T. Solution to Problem 3414, American Mathematical Monthly 37 (Dec. 1930), 558.
220. Lehmer, E. T. Solution to Problem 3803, American Mathematical Monthly 45 (Nov. 1938), 633-634.
221. Leighton, F. T., and M. Newman. "Positive Definite Matrices and Catalan Numbers," Proceedings of the AMS 79 (June 1980), 177-181.
222. Levine, J. "Note on the Number of Pairs of Nonintersecting Routes," Scripta Mathematica, 24 (1959), 335-338.
223. Linis, V. Solution to Problem E 2409, American Mathematical Monthly 81 (April 1974), 408.
224. Little, T. M. Solution to Problem E 1346, American Mathematical Monthly 66 (Sept. 1959), 590.
225. Liu, C. L. Introduction to Combinatorial Mathematics, McGraw-Hill, NewYork, 1968.
226. Liulevicius, A. "Homotopy Rigidity of Linear Actions: Characters Tell All," Bulletin of the AMS 84 (March 1978), 213-221.
227. Lobb. A. "Deriving the nth Catalan Number," Mathematical Gazette 83 (March 1999), 109-110.
228. Loève, M. "Random Walk," Probability Theory, D. van Nostrand, Princeton, New Jersey, 1963, 47-48.
229. Loney, S. L. Plane Trigonometry, Cambridge University Press, New York, 1933.
230. Lossers, O. P. Solution to Problem E 2520, American Mathematical Monthly 83 (May 1976), 383-384.
231. Lossers, O. P. Solution to Problem 11150, American Mathematical Monthly 114 (March 2007), 264-265.
232. Lovit, D. Solution to Problem 1739, Mathematics Magazine 80 (Feb. 2007), 80-81.
233. Mattson, H. F. Jr. Discrete Mathematics with Applications, Wiley, New York, 1993, 535-538.
234. Mays, M. E., and J.Wojciechowski. "A Determinant Property of Catalan Numbers," Discrete Mathematics 211 (2000), 125-133.
235. McCammond. J. "Noncrossing Partitions in Surprising Locations," American Mathematical Monthly 113 (Aug.-Sept. 2006), 598-610.
236. McKay, J. H. "The William Lowell Putnam Mathematical Competition," American Mathematical Monthly 73 (Aug.-Sept. 1966), 726-732.
237. Merlini, D. et al. "The Method of Coefficients," American Mathematical Monthly 114 (Jan. 2007), 40-57.
238. Miksa, F. L. et al. "Restricted Partitions of Finite Sets," Canadian Mathematics Bulletin 1 (May 1958), 87-96.
239. Moen, C. "Infinite Series with Binomial Coefficeints," Mathematics Magazine 64 (Feb. 1991), 53-55.
240. Mohanty, S. G. "Some Properties of Compositions and Their Application to the Ballot Problem," Canadian Mathemaitcs Bulletin 8 (1956), 359-372.
241. Moon, J. W. Topics on Tournaments, Holt, Rinehart and Winston, New York, 1968, 68-70.
242. Moon, J. W., and L. Moser. "Triangular Dissections of n-gons," Canadian Mathematics Bulletin 6 (1963), 175-178.
243. Moore, R. E. Problem 2752, American Mathematical Monthly 26 (Feb. 1919), 72.
244. More, Y. Problem 11165, American Mathematical Monthly 112 (June-July 2005), 568.
245. Moser, L. Solution to Problem E 1346, American Mathematical Monthly 66 (Sept. 1959), 591.
246. Moser, L. "Insolvability of 2n/n=(2a/a) (2b/b) ," Canadian Mathematics Bulletin 6 (1963), 167-169.
247. Moser, L., and W. Zayachkowski. "Lattice Paths with Diagonal Steps," Scripta Mathematica 26 (1963), 223-229.
248. Motzkin, T. "Relations between Hypersurface Cross Ratios, and a Combinatorial Formula for Partitions of a Polygon, for Permanent Preponderance, and for Nonassociative Products," Bulletin of the American Mathematical Society 54 (April 1948), 352-360.
249. Mullin, R. C. "On Counting Rooted Triangular Maps," Canadian Journal of Mathematics 17 (1965), 373-382.
250. Mullin, R. C., and R. G. Stanton. "A Map-Theoretic Approach to Davenport-Schinzel Sequences," Pacific Journal of Mathematics 40 (1972), 167-172.
251. Nederpelt, R. P. Solution to Problem E 1903, American Mathematical Monthly 79 (April 1972), 396.
252. Nelsen, R. B. Solution to Problem 1049, Mathematics Magazine 52 (Nov. 1979), 321-322.
253. Niven, I. "Interpretations of a Non-Associative Product," Mathematics of Choice, Random House, NewYork, 1965, 140-152.
254. Niven, I. "Formal Power Series," American Mathematical Monthly 75 (1969), 871-889.
255. Obituary. "H. Balakram," Journal of the Indian Mathematical Society 18 (June 1929), 71-72.
256. Odlyzko, A. M., and H. S. Wilf. "The Editor's Corner: n Coins in a Fountain," American Mathematical Monthly 95 (Nov. 1988), 840-843.
257. Olds, C. D. Problem E 760, American Mathematical Monthly 54 (Feb. 1947), 108.
258. Olds, C. D. Problem 4277, American Mathematical Monthly 55 (Jan. 1948), 34.
259. Ore, O. Problem 3954, American Mathematical Monthly 48 (April 1940), 245.
260. Otter, R. "The Number of Trees," Annals of Mathematics 49 (July 1948), 583-599.
261. Pennisi, L. L. "Expressions for π and π2," American Mathematical Monthly 62 (Nov. 1955), 653-654.
262. Pennisi, L. L. "A Method for Solving ∫ sin2n αx dx and ∫ cos2n αx dx," Mathematics Magazine 29 (May-June 1956), 271-272.
263. Petersen, J. Problem E 1700, American Mathematical Monthly 71 (May 1964), 555.
264. Philbrick, P. H. Solution to Problem 2, American Mathematical Monthly 1 (March 1894), 82.
265. Pollak, H. O. Solution to Problem 420, College Mathematics Journal 22 (Jan. 1991), 76.
266. Pólya, G. Mathematics and Plausible Reasoning, vol. 1, Princeton University Press, New Jersey, 1954.
267. Pólya, G. "On Picture-Writing," American Mathematical Monthly 63 (Dec. 1956), 689-697.
268. Poonen, B. Solution to Problem 1251, Mathematics Magazine 60 (Nov. 1987), 248.
269. Rainville, E. D. Solution to Problem 3674, American Mathematical Monthly 43 (Oct. 1935), 519.
270. Rainville, E. D. Solution to Problem 230, American Mathematical Monthly 29 (Nov.-Dec. 1955), 109-110.
271. Raney, G. N. "Functional Composition Patterns and Power Series Reversion," Transactions of the AMS 94 (1960), 441-451.
272. Renault, M. Solution to Problem 11071, American Mathematical Monthly 113 (May 2004), 460-461.
273. Renault, M. "Four proofs of the Ballot Theorem," Mathematics Magazine (Dec. 2007), 345-352.
274. Renault, M. "Lost (and Found) in Translation: Andreé's Actual Method and its Application to the Generalized Ballot Problem," American Mathematical Monthly 115 (April 2008), 358-363.
275. Rey, J. G. Problem 2070, Crux Mathematicorum 21 (1995), 236.
276. Rey, J. G. Problem 2070, Crux Mathematicorum 22 (1996), 279-281.
277. Richards, D. "Ballot Sequences and Restricted Permutations," Ars Combinatoria 25 (1988), 83-86.
278. Riddle, L. H. "An Occurrence of the Ballot Numbers in Operator Theory," American Mathematical Monthly 98 (Aug. 1991), 613-617.
279. Rinaldi, S., and Rogers, D. G. "Indecomposability: Polyominoes and Polyomino Tilings," Mathematics Gazette 92 (2008).
280. Riordan, J. An Introduction to Combinatorial Analysis, Princeton University Press, New Jersey, 1980, 125-139.
281. Riordan, J. Combinatorial Identities, Wiley, NewYork, 1968.
282. Riordan, J. "Ballots and Trees," Journal of Combinatorial Theory 6 (1969), 408-411.
283. Riordan, J. "A Note on Catalan Parentheses," American Mathematical Monthly 81 (Oct. 1973), 904-906.
284. Riordan, J. "The Distribution of Crossings of Chords Joining Pairs of 2n Points on a Circle," Mathematics of Computation 29 (1975), 215-222.
285. Rogers,D. G. "A Schröder Triangle: Three Combinatorial Problems," Australian Conference on Combinatorial Mathematics, Lecture Notes in Mathematics 622, Springer, Berlin, 1977, 175-196.
286. Rogers, D. G. "Pascal Triangles, Catalan Numbers, and Renewal Arrays," Discrete Mathematics 22 (1978), 301-310.
287. Rohatgi, V. K. "On Lattice Paths with Diagonal Steps," Canadian Mathematics Bulletin 7 (1964), 470-472.
288. Rohatgi, V. K. "Some Combinatorial Identities Involving Lattice Paths," American Mathematical Monthly 73 (1966), 507-508, 751.
289. Roselle, D. P. "An Algorithmic Approach to Davenport-Schinzel Sequences," Utilitas Mathematica 6 (1974), 91-93.
290. Roselle, D. P. "A Combinatorial Problem Involving q-Catalan Numbers," Notices of the AMS 21 (1974), A-609.
291. Rota, G. C. "Nomination for Ronald L. Graham for AMS President," Notices of the AMS 38 (Sep. 1991), 757-758.
292. Rousseau, C. C. Solution to Problem 1134, Pi Mu Epsilon Journal 12 (Spring 2007), 365-367.
293. Ruderman, H. D. Problem Q699, Mathematics Magazine 58 (Sept. 1985), 238,245.
294. Ruderman, H. D. Problem 1251, Mathematics Magazine 59 (Oct. 1986), 240.
295. Sandham, H. F. Problem 4519, American Mathematical Monthly 60 (Jan. 1953), 47.
296. Sandham, H. F. Solution to Problem 4519, American Mathematical Monthly 61 (Jan. 1953), 265.
297. Sands, A. D. "On Generalized Catalan Numbers," Discrete Mathematics 21 (1978), 219-221.
298. Schneider, J. E. Problem E 1600, American Mathematical Monthly 70 (May 1963), 569.
299. Schneider, R. Problem E 1854, The American Mathematical Monthly 73 (Jan. 1966), 83.
300. Schwatt, I. J. An Introduction to the Operators with Series, Chelsea, NewYork, 1924.
301. Schwenk,A. J. Solution to Problem 1213, American Mathematical Monthly 59 (April 1986), 115-116.
302. Scoville, R. "Some Properties of the Catalan Numbers," Notices of the AMS 21 (1974), A-602.
303. Seiffert, H. Problem 11172, American Mathematical Monthly 112 (Aug.-Sept. 2005), 655.
304. Shafer, R. E. Problem 6019, American Mathematical Monthly 82 (March 1975), 307.
305. Shapiro, L. W. "Rings and Catalan Numbers," American Mathematical Monthly 81 (1974), 940.
306. Shapiro, L. W. "Upper Triangular Rings, Ideals, and Catalan Numbers," American Mathematical Monthly 82 (1975), 634-637.
307. Shapiro, L. W. "Catalan Numbers and "Total Information" Numbers," Proceedings of the Sixth Southwestern Conference on Combinatorial Graph Theory and Computing, Florida Atlantic University, 1975, 531-539.
308. Shapiro, L. W. "A Catalan Triangle," Discrete Mathematics 14 (1976), 83-90.
309. Shapiro, L. W. "A Short Proof of an Identity of Touchard's Concerning Catalan Numbers," Journal of Combinatorial Theory, Series A, 20 (1976), 375-376.
310. Shapiro, L. W. "Positive Definite Matrices and Catalan Numbers, Revisited," Proceedings of the AMS 90 (March 1984), 488-496.
311. Shapiro, L. W., and W. Hamilton. "The Catalan Numbers Visit the World Series," Mathematics Magazine 66 (Feb. 1993), 20-22.
312. Shen, Y., and J. T. Shult. "Sailing around Binary Trees and Krusemeyer's Bijection," Mathematics Magazine 73 (June 2000), 216-220.
313. Sholander, M., and E. B. Leach. Problem E 2799, American Mathematical Monthly 86 (Nov. 1979), 785.
314. Silberger, D. M. "The Parity of the Integer (2n-2)!/n!(n-1)! ," Notices of the AMS 15 (1968), 615.
315. Silberger, D. M. "Occurrences of the Integer (2n-2)!/n!(n-1)! ," Roczniki Polskiego Towarzystwa Mathematics 13 (1969), 91-96.
316. Simion, R., and F. W. Schmidt. "Restricted Permutations," European Journal of Combinatorics 6 (1985), 383-406.
317. Simion, R., and D. Ullman. "On the Structure of the Lattice of Noncrossing Partitions," Discrete Mathematics, 98 (1991), 193-206.
318. Singmaster, D. Problem E 1896, American Mathematical Monthly 73 (June-July 1966), 665.
319. Singmaster, D. "An Elementary Evaluation of the Catalan Numbers," American Mathematical Monthly 85 (May 1978), 366-368.
320. Sloane, N. J. A. A Handbook of Integer Sequences, Academic Press, NewYork, 1973, 18-22.
321. Speigel, M. R. Problem E 995, American Mathematical Monthly 59 (June 1952), 411.
322. Squire, W. Problem 676, Mathematics Magazine 40 (Nov. 1967), 279.
323. Stanley, R. P. Enumerative Combinatorics, vol. 1, Wadsworth & Brooks/Cole, Monterey, California, 1986, 9-10, 52-63.
324. Stanley, R. P. Enumerative Combinatorics, vol. 2, Cambridge University Press, New York, 1999.
325. Stanley, R. P. "Catalan Addendum," .
326. Steelman, H. Solution to Problem 630, College Mathematics Journal 30 (May 1999), 234-235.
327. Steffen, K. Problem E 2174, American Mathematical Monthly 76 (May 1969), 553.
328. Stenger, A. Solution to Problem E 2520, American Mathematical Monthly 83 (May 1976), 383.
329. Strehl, V. "Enumeration of Alternating Permutations According to Peak Sets," Journal of Combinatorial Theory, Series A, 20 (1978) 238-240.
330. Sumner, J. S., and K. L. Dove. Solution to Problem 488, College Mathematics Journal 24 (Nov. 1993), 477.
331. Swylan, E. "Proving Numbers Catalan," Mathematical Gazette 86 (Nov. 2002), 460-463.
332. Szekeres, G. Solution to Problem 3954, American Mathematical Monthly 41 (Oct. 1941), 565.
333. Takács, L. Letter to the Editor, Mathematics Magazine 61 (Oct. 1988), 269.
334. Thielman, H. P. Problem 4510, American Mathematical Monthly 59 (Nov. 1952), 640.
335. van Hamme, L. Problem Q745, Mathematics Magazine 62 (April 1989), 137, 143.
336. van Lint, J. H. Lecture Notes in Mathematics, Springer-Verlag, NewYork, 1974.
337. Vaughn, H. E. Solution to Problem 3954, American Mathematical Monthly 41 (Oct. 1941), 564-565.
338. Vun, I., and P. Belcher. "Catalan Numbers," Mathematical Spectrum 29 (1996-1997), 3-5.
339. Wagner, R. J. Solution to Problem 436, College Mathematics Journal 22 (Nov. 1991), 444-445.
340. Wahlin, G. E. Solution to Problem 175, American Mathematical Monthly 18 (Feb. 1971), 41-43.
341. Walkup, D. W. "The Number of Plane Trees," Mathematika 19 (1972), 200-204.
342. Wang, E. T. H. Problem 420, The College Mathematics Journal 21 (Jan. 1990), 66.
343. Wang, E. T. H. Problem 1049, Mathematics Magazine 51 (Sept. 1978), 245.
344. Weinmann, A. Solution to Problem 5113, American Mathematical Monthly 71 (June-July, 1964), 691-692.
345. Weisstein, E. W. (ed.). CRC Concise Encyclopedia of Mathematics, Boca Raton, Florida.
346. Wells, M. B. Elements of Combinatorial Computing, Pergamon, New York, 1971.
347. West, J. "Generating Trees and the Catalan and Schröder Numbers," Discrete Mathematics 146 (1995), 247-262.
348. Wigner, E. P. "Characteristic Vectors of Bordered Matrices with Infinite Dimensions,"Annals of Mathematics 62 (Nov. 1955), 548-564.
349. Woan, W. et al. "The Catalan Numbers, the Lebesgue Integral, and 4 n-2," The American Mathematical Monthly 104 (Dec. 1997), 926-931.
350. Wong, B. C. Problem 3414, The American Mathematical Monthly 37 (March 1930), 157.
351. Yaglom, A. M., and I. M. Yaglom. Challenging Mathematical Problems with Elementary Solutions, vol. 1, Holden-Day, San Francisco, CA, 1964, 117-121.
352. Young, J. W. Problem 106, American Mathematical Monthly 9 (June-July 1902), 86. D. Zeitlin. Solution to Problem E 1346, American Mathematical Monthly 66 (Sept. 1959), 590.
353. Zerr, G. B. M. Solution to Problem 106, American Mathematical Monthly 9 (June-July 1902), 86.
354. Zerr, G. B. M. Solution to Problem 172, American Mathematical Monthly 17 (June-July 1910), 147.
355. Zucker, I. J. "On the Series and Related Series σk=1(2k/k)k-n," Journal of Number Theory 20 (1985), 92-102.