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  1. Home > Articles & Issues >
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  3. Combinatorial interp ...
Conference paper

Combinatorial interpretation and positivity of Kerov's character polynomials

Valentin Féray ORCID (1)
(1) Laboratoire d'Informatique Gaspard-Monge
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Proceedings
DOI
10.46298/dmtcs.3629
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https://about.hal.science/hal-authorisation-v1
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Combinatorial interpretation and positivity of Kerov's character polynomials

Valentin Féray ORCID (1)
(1) Laboratoire d'Informatique Gaspard-Monge
Abstract
English
Kerov's polynomials give irreducible character values of the symmetric group in term of the free cumulants of the associated Young diagram. Using a combinatorial approach with maps, we prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov.
French
Les polynômes de Kerov expriment les valeurs des caractères irréductibles du groupe symétrique en fonction des cumulants libres du diagramme de Young associé. Grâce à une approche combinatoire à base de cartes, nous prouvons dans cet article un résultat de positivité sur leurs coefficients, qui généralise une conjecture de S. Kerov.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Representations
  • symmetric group
  • maps
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