Generalized Energy Statistics and Kostka--Macdonald Polynomials

Details Generalized Energy Statistics and Kostka--Macdonald Polynomials Generalized Energy Statistics and Kostka--Macdonald Polynomials

2009-12-11

arxiv.org/abs/0912.2161v2

DMTCS proc. AN (2010) 343--354

Mathematics

Quantum Algebra

15 pages, typos corrected, French abstract added, version for publication in proceedings of FPSAC 2010.

Scientific paper

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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