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Generalized Energy Statistics and Kostka―Macdonald Polynomials

Abstract : We give an interpretation of the $t=1$ specialization of the modified Macdonald polynomial as a generating function of the energy statistics defined on the set of paths arising in the context of Box-Ball Systems (BBS-paths for short). We also introduce one parameter generalizations of the energy statistics on the set of BBS-paths which all, conjecturally, have the same distribution.
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https://hal.inria.fr/hal-01186282
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Anatol N. Kirillov, Reiho Sakamoto. Generalized Energy Statistics and Kostka―Macdonald Polynomials. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.343-354. ⟨hal-01186282⟩

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