×

zbMATH — the first resource for mathematics

Statistics for special \(q,t\)-Kostka polynomials. (English) Zbl 0886.05112
Summary: 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.

MSC:
05E05 Symmetric functions and generalizations
PDF BibTeX XML Cite
Full Text: DOI