Reiner And

We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict tableaux and Macdonald’s “7 variation” of Schur functions, the other relating to permutation statistics and Hilbert series from the invariant theory of GLn(Fq).