Anatol N. Kirillov ; Reiho Sakamoto - Generalized Energy Statistics and Kostka―Macdonald Polynomials

dmtcs:2854 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2854
Generalized Energy Statistics and Kostka―Macdonald PolynomialsArticle

Authors: Anatol N. Kirillov 1; Reiho Sakamoto 2

  • 1 Research Institute for Mathematical Sciences
  • 2 Department of Physics [Tokyo]

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.

https://doi.org/10.46298/dmtcs.2854
Source: HAL:hal-01186282v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: modified Macdonald polynomials,box-ball systems,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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