Generalized Energy Statistics and Kostka--Macdonald Polynomials.

link: http://arxiv.org/abs/0912.2161
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 generalization of the energy statistics on the set
of BBS-paths which all, conjecturally, have the same distribution.