Ramsey theory before ramsey, prehistory and early history: An essay in 13 parts

Progress in Mathematics

Volumn 285, Issue , 2011, Pages 1-26

  Soifer, Alexander ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84969959335     PISSN: 07431643     EISSN: 2296505X     Source Type: Book Series    
DOI: 10.1007/978-0-8176-8092-3_1     Document Type: Chapter

References (53)

1. Arnautov, V.I., Nediskretnaya Topologizuemost Schetnykh Kolets, (Russian), Dokl. Akad. Nauk SSSR 191 (1970), 747-750. English Translation: Nondiscrete topologizability of countable rings, Soviet Math. Dokl. 11 (1970), 423-426.
2. Brauer, A., Über Sequenzen von Potenzresten, Sitzunberichte de Preussischen Akademie der Wissenschaften, Physicalisch-Mathematische Klasse, Berlin, 1928, 9-16.
3. Brauer, A., Combinatorial methods in the distribution ofkth power residues, Combinatorial Mathematics and Its Applications; Proceedings of the Conference, University of North Carolina, 14-37, 1969.
4. Brauer, A., Gedenkrede aufIssai Schur, in Issai Schur. Gesammelte Abhandlungen, vol. 1, Springer, Berlin, 1973, v-xiv.
5. de Bruijn, N.G., Letter to P. Erdős, August 18, 1947.
6. Bruijn, N.G. de and Erdős, P., A colour problem for infinite graphs and a problem in the theory of relations, Indagationes Math. 13 (1951), 369-373.
7. Burkill, H. and Mirsky, L., Monotonicity, J. Math. Anal. Appl. 41 (1973), 391-410.
8. Chung, F. and Graham, R.L., Forced convex n-gons in the plane, Discrete Comput. Geom. 19 (1998), 3677-371.
9. Dickson, L.E., On the Last Theorem of Fermat, Quart. J. Pure Appl. Math. 40 (1908), 27-45.
10. Erdős, P., Letter to N. G. de Bruijn, August 4, 1947.
11. Erdős, P., Some unsolved problems, Michigan Math. J. 4 (1957), 291-300.
12. Erdős, P., Some unsolved problems, Magyar tudomanyos akademia mathematikai kutato intezetenek közlemenyel 6 ser. A(1-2) (1961), 221-254.
13. Erdős, P., Nekotorye Nereshennye Problemy (Some unsolved problems), Matematika 7(4) (1963), 109-143. (A Russian translation of [E61.22])
14. Erdős, P., On the application of combinatorial analysis to number theory, geometry and analysis, Actes du Congrès International des Mathematiciens (Nice, 1970), Tome 3, pp. 201-210, Gauthier-Villars, Paris, 1971.
15. Erdős, P., Problems and results on combinatorial number theory, A survey of Combinatorial Theory (Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colorado, 1971), 117-138, North-Holland, Amsterdam, 1973.
16. Erdős, P., Problems and results in combinatorial analysis, Colloquio Internacionale sulle Teorie Combinatorie (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 3-17, Accad. Naz. Lincei, Rome, 1976.
17. Erdős, P., On the combinatorial problems which I would most like to see solved, Combinatorica 1 (1981), 25-42.
18. Erdős, P., Some problems and results in number theory, Number Theory and Combinatorics, Japan 1984 (Tokyo, Okayama and Kyoto, 1984), pp. 65-87, World Scientific, Singapore, 1985.
19. Erdős, P., Obituary of my friend and coauthor Tibor Gallai, Geombinatorics II (1) (1992), 5-6; corrections: II(2), 1992, 37.
20. Erdős, P. and Graham, R., Old and New Problems and Results in Combinatorial Number Theory, L’Enseignement Mathématique, Université de Genève, 1980.
21. Erdős, P. and Szekeres, G., A combinatorial problem in geometry, Compositio Math., 2 (1935), 463-470.
22. Erdős, P. and Turán, P., On Some Sequences of Integers, J. Lond. Math. Soc. 11 (1936), 261-264.
23. Garsia, A., Manuscript, Fall 1958, 10 pp.
24. Graham, R.L., Recent developments in Ramsey theory. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 1555-1567, PWN, Warsaw, 1984.
25. Graham, R.L. and Nesetril, J., Ramsey theory and Paul Erdős, in Paul Erdős and his Mathematics II, ed. by G. Halász, et al., Springer, Budapest, 2002, 339-365.
26. Graham, R.L. and Rothschild, B.L., Ramsey’s theorem for n-parameter sets, Trans. Am. Math. Soc. 159 (1971), 257-292.
27. Graham, R.L., Rothschild, B.L., and Spencer, J.H., Ramsey Theory, 1st Edition, John Wiley & Sons, New York, 1980.
28. Graham, R.L., Rothschild, B.L., and Spencer, J.H., Ramsey Theory, 2nd Edition, John Wiley & Sons, New York, 1990.
29. Greenwood, R.E. and Gleason, A.M., Combinatorial relations and chromatic graphs, Can. J. Math. 7 (1955), 1-7.
30. Hilbert, D., Ueber die Irreducibilität ganzer rationaler Functionen mit ganzzahligen Coefficienten, J. Reine Angew. Math. 110 (1892), 104-129.
31. Hindman, N., Finite Sums from Sequences within Cells of a Partition of N, J. Combin. Theory Ser. A 17 (1974), 1-11.
32. Khinchin, A.Y., Tri Zhemchuzhiny Teorii Chisel, Gos. Izd-vo tekhn.-teoret, lit-ry, Moskva, 1947 (Russian).
33. Khinchin, A.Y., Tri Zhemchuzhiny Teorii Chisel, Gos. Izd-vo tekhn.-teoret, lit-ry, 2nd ed., Moskva, 1948 (Russian).
34. Chintschin, A.J., Drei Pearlen der Zahlentheorie, Akademie Verlag, Berlin, 1951.
35. Khinchin, A.Y., Three Pearls of Number Theory, Graylock, Rochester, New York, 1952.
36. Mirsky, L., The combinatorics of arbitrary partitions, Bull. Inst. Math. 11 (1975), 6-9.
37. Rado, R., Studien zur Kombinatorik, Math. Zeitschrift 36 (1933), 424-480.
38. Rado, R., Note on Combinatorial Analysis, Proc. Lond. Math. Soc. 48(2) (1943), 122-160.
39. Ramsey, F.P., On a problem of formal logic, Proc. Lond. Math. Soc. Ser 2 30(4) (1930), 338-384.
40. Roth, K.F., On certain sets of integers, J. Lond. Math. Soc. 28 (1953), 104-109.
41. Sanders, J.H., A Generalization of Schur’s Theorem, Ph.D. Dissertation, Yale University, 1968.
42. Schur, I., Über die Kongruenzx m+y m≡z m(mod.p), Jahresbericht der Deutschen Mathematiker-Vereinigung 25 (1916), 114-117.
43. Seidenberg, A., A simple proof of Erdős and Szekeres, J. London Math. Soc. 34 (1959), 352.
44. Shelah, S. and Soifer, A., Axiom of choice and chromatic number of the plane, J.Combin. Theory Ser. A 103 (2003), 387-391.
45. Soifer, A. and Shelah, S., Axiom of choice and chromatic number: An example on the plane, J. Combin. Theory Ser. A 2(105) (2004), 359-364.
46. Skolem, T., Ein Kombinatorische Satz mit Anwendung auf ein Logisches Entscheidungsproblem, Fundamenta Math. 20 (1933), 254-261.
47. Soifer, A., The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators, Springer, New York, 2009.MATH
48. Szemerédi, E., On sets of integers containing no four elements in arithmetic progression, Acta Math. Acad. Sci. Hungar. 20 (1969), 89-104.
49. Szemerédi, E., On sets of integers containing no k elements in arithmetic progression, Acta Arithmetica XXVII (1975), 199-245.
50. Tóth, G. and Valtr, P., The Erdős-Szekeres theorem, upper bounds and generalizations, in Discrete and Computational Geometry - Papers from the MSRI Special Program, ed. by J.E. Goodman et al., MSRI Publications 52, Cambridge University Press, Cambridge, 2005, 557-568.
51. van der Waerden, B.L., Beweis einer audetschen Vermutung, Nieuw Archief voor Wiskunde 15 (1927), 212-216.
52. van der Waerden, B.L., How the proof of Baudet’s conjecture was found, in Studies in Pure Mathematics, ed. by L. Mirsky, Academic Press, London, 1971, 251-260.
53. Witt, E., Ein kombinatorischer Satz der Elementargeometrie, Mathematische Nachrichten 6 (1952), 261-262.