Soojin Cho ; Eun-Kyoung Jung ; Dongho Moon
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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)
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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 2
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Soojin Cho;Eun-Kyoung Jung;Dongho Moon
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.
Soojin Cho;Eun-Kyoung Jung;Dongho Moon, 2011, A Hive-Model Proof of the Second Reduction Formula of Littlewood-Richardson Coefficients, Annals of Combinatorics, 15, 2, pp. 223-231, 10.1007/s00026-011-0091-8.