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)Article

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]

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