Article
Combinatorial proof for a stability property of plethysm coefficients
Author/s | Colmenarejo Hernando, Laura
Briand, Emmanuel ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2014 |
Deposit Date | 2019-07-02 |
Published in |
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Abstract | Plethysm coefficients are important structural constants in the representation the-
ory of the symmetric groups and general linear groups. Remarkably, some sequences
of plethysm coefficients stabilize (they are ultimately ... Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose plethysm coefficients as a alternating sum of terms counting integer points in poly- topes, and exhibit bijections between these sets of integer points. |
Project ID. | MTM2010–19336
![]() FQM–333 ![]() P12–FQM–2696 ![]() |
Citation | Colmenarejo Hernando, L. y Briand, E. (2014). Combinatorial proof for a stability property of plethysm coefficients. Electronic Notes in Discrete Mathematics, 46 (september 2014), 43-50. |
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