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Combinatorial proof for a stability property of plethysm coefficients

 

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Opened Access Combinatorial proof for a stability property of plethysm coefficients
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Author: Colmenarejo Hernando, Laura
Briand, Emmanuel
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2014
Published in: Electronic Notes in Discrete Mathematics, 46 (september 2014), 43-50.
Document type: Article
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 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.
Cite: 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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URI: https://hdl.handle.net/11441/87750

DOI: 10.1016/j.endm.2014.08.007

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