English

Generalized Energy Statistics and Kostka--Macdonald Polynomials

Quantum Algebra 2010-07-27 v2

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.

Cite

@article{arxiv.0912.2161,
  title  = {Generalized Energy Statistics and Kostka--Macdonald Polynomials},
  author = {Anatol N. Kirillov and Reiho Sakamoto},
  journal= {arXiv preprint arXiv:0912.2161},
  year   = {2010}
}

Comments

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

R2 v1 2026-06-21T14:22:32.280Z