Soojin Cho ; EunKyoung Jung ; Dongho Moon

Reduction formulae from the factorization Theorem of LittlewoodRichardson 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 LittlewoodRichardson polynomials by King, Tollu and Toumazet
Authors: Soojin Cho ^{1}; EunKyoung Jung ^{1}; Dongho Moon ^{2}
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Soojin Cho;EunKyoung 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 LittlewoodRichardson 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 $r=1, 2, n2$ in terms of tableaux and the proof for the classical reduction formula of the second type in terms of hives are new.
Cho, Soojin; Jung, EunKyoung; Moon, Dongho, 2011, A HiveModel Proof Of The Second Reduction Formula Of LittlewoodRichardson Coefficients, Annals Of Combinatorics, 15, 2, pp. 223231, 10.1007/s0002601100918.