Discrete Mathematics & Theoretical Computer Science |

- 1 Department of mathematics [Philadelphie]
- 2 Department of Mathematics [Univ California Davis]

Using the expansion of the inverse of the Kostka matrix in terms of tabloids as presented by Eğecioğlu and Remmel, we show that the fusion coefficients can be expressed as an alternating sum over cylindric tableaux. Cylindric tableaux are skew tableaux with a certain cyclic symmetry. When the skew shape of the tableau has a cutting point, meaning that the cylindric skew shape is not connected, or if its weight has at most two parts, we give a positive combinatorial formula for the fusion coefficients. The proof uses a slight modification of a sign-reversing involution introduced by Remmel and Shimozono. We discuss how this approach may work in general.

Source: HAL:hal-01283115v1

Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)

Section: Proceedings

Published on: January 1, 2012

Imported on: January 31, 2017

Keywords: Gromov―Witten invariants, Littlewood―Richardson coefficients, (inverse) Kostka matrix, crystal graphs, cylindric tableaux, sign-reversing involution,fusion coefficients,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
*Affine Combinatorics*; Funder: National Science Foundation; Code: 1001256*Refined symmetric functions and affine analogs in combinatorics*; Funder: National Science Foundation; Code: 0638625*FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects*; Funder: National Science Foundation; Code: 0652641*FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects*; Funder: National Science Foundation; Code: 0652652*Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials*; Funder: National Science Foundation; Code: 1001898

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