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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1264811-3
PII: S 0002-9939(1995)1264811-3
Keywords: Two-parameter Kostka matrix, rigged configurations
Article copyright: © Copyright 1995 American Mathematical Society