A Bijection on Ordered Trees and Its Consequences

Journal of Combinatorial Theory. Series A

Volumn 90, Issue 1, 2000, Pages 210-215

  Deutsch, Emeric ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Bijection; Degree of a node; Level of a node; Ordered trees

Indexed keywords

EID: 0347560392     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1999.3027     Document Type: Article

References (17)

1. B. Dasarathy and C. Yang, A transformation on ordered trees, Comput. J. 23, No. 2 (1980), 161-164.
2. N. Dershowitz and S. Zaks, Enumerations of ordered trees, Discrete Math. 31 (1980), 9-28.
3. N. Dershowitz and S. Zaks, Applied tree enumerations, in "Lecture Notes in Computer Science," Vol. 112, pp. 180-193, Springer-Verlag, Berlin, 1981.
4. R. Donaghey, Restricted plane tree representations of four Motzkin-Catalan equations, J. Combin. Theory Ser. B 23 (1977), 114-121.
5. R. Donaghey and L. W. Shapiro, Motzkin numbers, J. Combin. Theory Ser. A 23 (1977), 291-301.
6. R. L. Graham, D. E. Knuth, and O. Patashnik, "Concrete Mathematics," 2nd ed., Addison-Wesley, Reading, MA, 1994.
7. D. A. Klarner, Correspondences between plane trees and binary sequences, J. Combin. Theory 9 (1970), 401-411.
8. G. Kreweras, Joint distributions of three descriptive parameters of bridges, in "Lecture Notes in Mathematics," Vol. 1234, pp. 177-191, Springer-Verlag, Berlin, 1986.
9. A. Kuznetsov, I. Pak, and A. Postnikov, Trees associated with the Motzkin numbers, J. Combin. Theory Ser. A 76 (1996), 145-147.
10. T. Motzkin, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for nonassociative products, Bull. Amer. Math. Soc. 54 (1948), 352-360.
11. J. Riordan, Enumeration of plane trees by branches and endpoints, J. Combin. Theory Ser. A 19 (1975), 214-222.
12. R. Sedgewick and P. Flajolet, "An Introduction to the Analysis of Algorithms," Addison-Wesley, Reading, MA, 1996.
13. R. A. Sulanke, A symmetric variation of a distribution of Kreweras and Poupard, J. Statist. Plann. Inference 34 (1993), 291-303.
14. R. A. Sulanke, Catalan path statistics having the Narayana distribution, Discrete Math. 180 (1998), 369-389.
15. R. A. Sulanke, Constraint-sensitive Catalan path statistics having the Narayana distribution, Discrete Math. 204 (1999), 397-414.
16. H. S. Wilf, "Generatingfunctionology," 2nd ed., Academic Press, New York, 1994.
17. D. Zeilberger, Six études in generating functions, Internat. J. Comput. Math. 29 (1989), 201-215.