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The $q$-binomial theorem states that $$ \prod_{k=0}^{n-1}(1+q^kt) = \sum_{k=0}^n q^{\binom k2}{n\brack k}_q t^k. $$ This identity is a $q$-analogue of the binomial theorem $$ (1+t)^n = \sum_{k=0}^n \...

I am interested in the field with one element. I am thus interested in combinatorial interpretations of the Gaussian binomial coefficients. Richard Stanley's "Enumerative combinatorics" mentions ...

I have already known QPermutationDerangement: It describes the distribution $$ d_n(q)=\sum_{\sigma \in D_n} q^{\operatorname{maj}(\sigma)} $$ Where we sum over all derangements of an $n$ element set. ...