Soojin Cho ; Eun-Kyoung Jung ; Dongho Moon - Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and Toumazet

dmtcs:3592 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3592
Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and ToumazetArticle

Authors: Soojin Cho 1; Eun-Kyoung Jung 1; Dongho Moon ORCID2

  • 1 Department of Mathematics [Ajou]
  • 2 Department of Applied Mathematics

The factorization theorem by King, Tollu and Toumazet gives four different reduction formulae of Littlewood-Richardson coefficients. One of them is the classical reduction formula of the first type while others are new. Moreover, the classical reduction formula of the second type is not a special case of KTT theorem. We give combinatorial proofs of reduction formulae in terms of tableaux or hives. The proofs for the cases $r=1, 2, n-2$ in terms of tableaux and the proof for the classical reduction formula of the second type in terms of hives are new.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: Reduction formulae,KTT factorization theorem,Littlewood-Richardson coefficients,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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