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Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and Toumazet

Abstract : 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.
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Soojin Cho, Eun-Kyoung Jung, Dongho Moon. Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and Toumazet. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.483-494. ⟨hal-01185125⟩

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