Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Counting tournament score sequences
HTML articles powered by AMS MathViewer

by Anders Claesson, Mark Dukes, Atli Fannar Franklín and Sigurður Örn Stefánsson
Proc. Amer. Math. Soc. 151 (2023), 3691-3704
DOI: https://doi.org/10.1090/proc/16425
Published electronically: May 5, 2023

Abstract:

The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old [Quart. J. Math. 49 (1920), pp. 1–36]. In 2013 Hanna conjectured a surprising and elegant recursion for these numbers. We settle this conjecture in the affirmative by showing that it is a corollary to our main theorem, which is a factorization of the generating function for score sequences with a distinguished index. We also derive a closed formula and a quadratic time algorithm for counting score sequences.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 05A15, 05A19
  • Retrieve articles in all journals with MSC (2020): 05A15, 05A19
Bibliographic Information
  • Anders Claesson
  • Affiliation: Department of Mathematics, University of Iceland, Reykjavik, Iceland
  • MR Author ID: 684271
  • ORCID: 0000-0001-5797-8673
  • Email: akc@hi.is
  • Mark Dukes
  • Affiliation: School of Mathematics and Statistics, University College Dublin, Dublin, Ireland
  • MR Author ID: 696771
  • ORCID: 0000-0002-2779-2680
  • Email: mark.dukes@ucd.ie
  • Atli Fannar Franklín
  • Affiliation: Department of Mathematics, University of Iceland, Reykjavik, Iceland
  • Email: aff6@hi.is
  • Sigurður Örn Stefánsson
  • Affiliation: Department of Mathematics, University of Iceland, Reykjavik, Iceland
  • Email: sigurdur@hi.is
  • Received by editor(s): September 30, 2022
  • Received by editor(s) in revised form: January 4, 2023, January 13, 2023, and January 14, 2023
  • Published electronically: May 5, 2023
  • Communicated by: Isabella Novik
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 3691-3704
  • MSC (2020): Primary 05A15, 05A19
  • DOI: https://doi.org/10.1090/proc/16425
  • MathSciNet review: 4607616