Combinatorial interpretation and positivity of Kerov's character polynomials

Valentin Féray

doi:10.46298/dmtcs.3629

Valentin Féray - Combinatorial interpretation and positivity of Kerov's character polynomials

dmtcs:3629 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3629

Combinatorial interpretation and positivity of Kerov's character polynomialsConference paper

Authors: Valentin Féray ¹

1 Laboratoire d'Informatique Gaspard-Monge

[en]
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.

[fr]
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.

https://doi.org/10.46298/dmtcs.3629

Source: HAL:hal-01185164v1

Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Representations, symmetric group, maps

Bibliographic References

11 Documents citing this article

Shinji Koshida, 2024, Planar algebras for the Young graph and the Khovanov Heisenberg category, International Journal of Mathematics, 36, 06, 10.1142/s0129167x25500028.

Shinji Koshida, 2023, Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category, Journal of Combinatorial Theory Series A, 196, pp. 105735, 10.1016/j.jcta.2023.105735, https://doi.org/10.1016/j.jcta.2023.105735.

Mikołaj Marciniak, 2022, Quadratic Coefficients of Goulden–Rattan Character Polynomials, Annals of Combinatorics, 27, 1, pp. 109-128, 10.1007/s00026-022-00611-5, https://doi.org/10.1007/s00026-022-00611-5.

Valentin Féray, 2020, Cyclic inclusion-exclusion and the kernel of P -partitions, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings, 28th..., 10.46298/dmtcs.6344, https://doi.org/10.46298/dmtcs.6344.

Per Alexandersson;Valentin Féray, 2017, Shifted symmetric functions and multirectangular coordinates of Young diagrams, arXiv (Cornell University), 483, pp. 262-305, 10.1016/j.jalgebra.2017.03.036, http://arxiv.org/abs/1608.02447.

Maciej Dołęga;Valentin Féray, 2016, Gaussian fluctuations of Young diagrams and structure constants of Jack characters, arXiv (Cornell University), 165, 7, 10.1215/00127094-3449566, http://arxiv.org/abs/1402.4615.

Valentin Féray, 2015, Cyclic Inclusion-Exclusion, SIAM Journal on Discrete Mathematics, 29, 4, pp. 2284-2311, 10.1137/140991364.

Jean-Christophe Aval;Valentin Féray;Jean-Christophe Novelli;Jean-Yves Thibon, 2014, Quasi-symmetric functions as polynomial functions on Young diagrams, Journal of Algebraic Combinatorics, 41, 3, pp. 669-706, 10.1007/s10801-014-0549-y, https://doi.org/10.1007/s10801-014-0549-y.

Valentin Féray;Piotr Śniady, 2011, Zonal polynomials via Stanleyʼs coordinates and free cumulants, arXiv (Cornell University), 334, 1, pp. 338-373, 10.1016/j.jalgebra.2011.03.008, http://arxiv.org/abs/1005.0316.

Maciej Dołęga;Valentin Féray;Piotr Śniady, 2010, Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations, arXiv (Cornell University), 225, 1, pp. 81-120, 10.1016/j.aim.2010.02.011, http://arxiv.org/abs/0810.3209.

P. Petrullo;D. Senato, 2010, Explicit formulae for Kerov polynomials, Journal of Algebraic Combinatorics, 33, 1, pp. 141-151, 10.1007/s10801-010-0239-3, https://doi.org/10.1007/s10801-010-0239-3.

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