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Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and Toumazet
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008) Cet article a éte moissonné depuis la source Episciences

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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. 
@article{DMTCS_2008_special_255_a0,
     author = {Cho, Soojin and Jung, Eun-Kyoung and Moon, Dongho},
     title = {Reduction formulae from the factorization {Theorem} of {Littlewood-Richardson} polynomials by {King,} {Tollu} and {Toumazet}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2008},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     doi = {10.46298/dmtcs.3592},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3592/}
}
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Cho, Soojin; Jung, Eun-Kyoung; Moon, Dongho. Reduction formulae from the factorization Theorem of Littlewood-Richardson polynomials by King, Tollu and Toumazet. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi: 10.46298/dmtcs.3592

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