Emmanuel Briand ; Rosa Orellana ; Mercedes Rosas - Quasipolynomial formulas for the Kronecker coefficients indexed by two two―row shapes (extended abstract)

dmtcs:2735 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2735
Quasipolynomial formulas for the Kronecker coefficients indexed by two two―row shapes (extended abstract)

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

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

We show that the Kronecker coefficients indexed by two two―row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. These new formulas are obtained from analogous formulas for the corresponding reduced Kronecker coefficients and a formula recovering the Kronecker coefficients from the reduced Kronecker coefficients. As an application, we characterize all the Kronecker coefficients indexed by two two-row shapes that are equal to zero. This allowed us to disprove a conjecture of Mulmuley about the behavior of the stretching functions attached to the Kronecker coefficients.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Kronecker coefficients,internal product of symmetric functions,Saturation properties,Representations of the symmetric group,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV math/0404353
Source : ScholeXplorer IsRelatedTo DOI 10.2977/prims/1145475445
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0404353
  • 10.2977/prims/1145475445
  • 10.2977/prims/1145475445
  • math/0404353
  • 10.48550/arxiv.math/0404353
An Invitation to the Generalized Saturation Conjecture

1 Document citing this article

Consultation statistics

This page has been seen 140 times.
This article's PDF has been downloaded 134 times.