Factorisation of Littlewood-Richardson coefficients |
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Authors: | Ronald C King |
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Institution: | a School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK b Laboratoire d'Informatique de Paris-Nord, CNRS UMR 7030, Université Paris 13, 93430 Villetaneuse, France |
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Abstract: | The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients. |
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Keywords: | Littlewood-Richardson coefficients Hive model Horn inequalities Puzzles Factorisation LR-polynomials |
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