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New fermionic formula for unrestricted Kostka polynomials

Lipika Deka·Anne Schilling
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Abstract

A new fermionic formula for the unrestricted Kostka polynomials of type $A_{n-1}^{(1)}$ is presented. This formula is different from the one given by Hatayama et al. and is valid for all crystal paths based on Kirillov-Reshetihkin modules, not just for the symmetric and anti-symmetric case. The fermionic formula can be interpreted in terms of a new set of unrestricted rigged configurations. For the proof a statistics preserving bijection from this new set of unrestricted rigged configurations to the set of unrestricted crystal paths is given which generalizes a bijection of Kirillov and Reshetikhin.

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Lipika Deka, Anne Schilling. 2005-09-08. New fermionic formula for unrestricted Kostka polynomials. https://doi.org/10.1016/j.jcta.2006.01.003

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