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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:
 500000 Symmetric functions and generalizations
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