Emmanuel Briand ; Rosa Orellana ; Mercedes Rosas - Invariance properties for coefficients of symmetric functions

dmtcs:2464 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2464
Invariance properties for coefficients of symmetric functionsConference paper

Authors: Emmanuel Briand 1; Rosa Orellana 2; Mercedes Rosas 3

  • 1 Department of Applied Mathematics I [Sevilla]
  • 2 Department of Mathematics [Dartmouth]
  • 3 Departamento de Algebra [Sevilla]

[en]
We show that several of the main structural constants for symmetric functions (Littlewood-Richardsoncoefficients, Kronecker coefficients, plethysm coefficients, and the Kostka–Foulkes polynomials) share invarianceproperties related to the operations of taking complements with respect to rectangles and adding rectangles.

[fr]
Nous montrons que plusieurs des principales constantes de structure de la théorie des fonctions symétriques(les coefficients de Littlewood–Richardson, les coefficients de Kronecker, les coefficients du pléthysme, et les polynômesde Kostka–Foulkes) ont en commun des symétries décrites par des opérations de complémentation dans des rectangleset d’ajout de rectangles pour les partitions qui les étiquettent.

https://doi.org/10.46298/dmtcs.2464
Source: HAL:hal-01337788v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients, Kostka coefficients
Licence: Attribution 4.0 International (CC BY 4.0)

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