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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Statistics for special $ q,t$-Kostka polynomials

Author: Susanna Fishel
Journal: Proc. Amer. Math. Soc. 123 (1995), 2961-2969
MSC: Primary 05E05
MathSciNet review: 1264811
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Abstract: Kirillov and Reshetikhin introduced rigged configurations as a new way to calculate the entries $ {K_{\lambda \mu }}(t)$ of the Kostka matrix. Macdonald defined the two-parameter Kostka matrix whose entries $ {K_{\lambda \mu }}(q,t)$ generalize $ {K_{\lambda \mu }}(t)$. We use rigged configurations and a formula of Stembridge to provide a combinatorial interpretation of $ {K_{\lambda \mu }}(q,t)$ in the case where $ \mu $ is a partition with no more than two columns. In particular, we show that in this case, $ {K_{\lambda \mu }}(q,t)$ has nonnegative coefficients.

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Keywords: Two-parameter Kostka matrix, rigged configurations
Article copyright: © Copyright 1995 American Mathematical Society

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