Some $n$-space $q$-binomial theorem extensions and similar identities

Abstract

We give an $n$-space generalized $q$-binomial theorem, and some new $q$ series identities that resemble the traditional $q$ series partition generating functions. These identities enumerate stepping stone weighted vector partitions.

18 pages, including a figure illustrating a Vector Partition theorem. The 2-D version at least, and possibly other cases from this paper, have been taken up by the Physics staff in a Statistical Mechanics context and will be citing the present article