Multi-partition analogue of q-binomial coefficients

Abstract

We introduce the multi-Gaussian polynomial [Formula: see text], a multi-partition analogue of the Gaussian polynomial (also known as [Formula: see text]-binomial coefficient), as the generating function for certain restricted multi-color partitions. We study basic properties of multi-Gaussian polynomials and non-symmetric properties of [Formula: see text]. We also derive a Sylvester-type identity and its application.