Counting tournament score sequences
EUROCOMB’23
290–297
Max Alekseyev. https://oeis.org/A145855/a145855.txt, 2008.
Arthur Cayley. A theorem on trees, volume 13 of Cambridge Library Collection - Mathematics, pages 26--28. Cambridge University Press, 2009.
Shane Chern. An extension of a formula of Jovovic. Integers, 19:Paper No. A47, 2019.
Anders Claesson, Mark Dukes, Atli Fannar Franklín, and Sigurdur Örn Stefánsson. Counting tournament score sequences. Proceedings of the American Mathematical Society, to appear. doi:10.1090/proc/16425. arXiv:2209.03925.
https://doi.org/10.1090/proc/16425
P. Erdős, A. Ginzburg, and A. Ziv. Theorem in the additive number theory. Bull. Res. Council Israel Sect. F, 10F(1):41-43, 1961.
Frank Harary and Leo Moser. The theory of round robin tournaments. Amer. Math. Monthly, 73:231-246, 1966.
https://doi.org/10.1080/00029890.1966.11970749
OEIS Foundation Inc. The Online Encyclopedia of Integer Sequences. https://oeis.org, 2021.
Daniel J Kleitman and Kenneth J Winston. Forests and score vectors. Combinatorica, 1(1):49-54, 1981.
https://doi.org/10.1007/BF02579176
H. G. Landau. On dominance relations and the structure of animal societies: III. The condition for a score structure. Bull. Math. Biophys., 15:143-148, 1953.
https://doi.org/10.1007/BF02476378
P. A. MacMahon. An American tournament treated by the calculus of symmetric functions. Quart. J. Math., 49:1-36, 1920. Reprinted in Percy Alexander MacMahon Collected Papers, Volume I, George E. Andrews, ed., MIT Press, 1978.
T. V. Narayana and D. H. Bent. Computation of the number of score sequences in round-robin tournaments. Can. Math. Bull, 7(1):133-136, 1964.
https://doi.org/10.4153/CMB-1964-015-1
John Riordan. The number of score sequences in tournaments. J. Combinatorial Theory, 5:87-89, 1968.
https://doi.org/10.1016/S0021-9800(68)80032-8
John Riordan. Erratum: "The number of score sequences in tournaments". J. Combinatorial Theory, 6:226, 1969.
https://doi.org/10.1016/S0021-9800(69)80130-4
Richard P. Stanley. Decompositions of rational convex polytopes. In J. Srivastava, editor, Combinatorial Mathematics, Optimal Designs and Their Applications, volume 6 of Annals of Discrete Mathematics, pages 333-342. Elsevier, 1980.
https://doi.org/10.1016/S0167-5060(08)70717-9
Paul K. Stockmeyer. Counting various classes of tournament score sequences. arXiv:2202.05238v1, 2022.
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