q,t Analogs of well-known
combinatorial sequences

Here are 4 q,t analogs that are related to Macdonald polynomials and Diagonal Harmonics

Open problem:  Find a combinatorial interpretation for ANY of the q,t analogs of the known sequences listed below

Open problem: Prove that ANY of the q,t analogs of the sequences listed below are polynomials with non-negative integer coefficients (the polynomiality has already been settled, but new proofs are always welcome).

Maple programs exist on this web site if you would like to compute and experiment with these q,t-polynomials (see nabla.html).

Sequences with a dependence on an extra parameter \mu