Geodesic
The stability of the Kronecker product of Schur functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010) Cet article a éte moissonné depuis la source Episciences

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In the late 1930's Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For $n$ large enough, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree $n$ do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n when this stable expansion is reached. We also compute two new bounds for the stabilization of a particular coefficient of such a product. Given partitions $\alpha$ and $\beta$, we give bounds for all the parts of any partition $\gamma$ such that the corresponding Kronecker coefficient is nonzero. Finally, we also show that the reduced Kronecker coefficients are structure coefficients for the Heisenberg product introduced by Aguiar, Ferrer and Moreira. 
@article{DMTCS_2010_special_259_a67,
     author = {Briand, Emmanuel and Orellana, Rosa and Rosas, Mercedes},
     title = {The stability of the {Kronecker} product of {Schur} functions},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2010},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     doi = {10.46298/dmtcs.2872},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2872/}
}
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%D 2010
%V DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
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Briand, Emmanuel; Orellana, Rosa; Rosas, Mercedes. The stability of the Kronecker product of Schur functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi: 10.46298/dmtcs.2872

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