GENERALIZED BINOMIAL COEFFICIENTS AND THE SUBSET-SUBSPACE PROBLEM

Generalized binomial coefficients of the first and second kind are def ined in terms of object selection with and without repetition from wei ghted boxes. The combinatorial definition unifies the binomial coeffic ients, the Gaussian coefficients, and the Stirling numbers and their r ecurrence relations under a common interpretation. Combinatorial proof s for some Gaussian coefficient identities are derived and shown to re duce to the ordinary binomial coefficients when q = 1. This approach p rovides a different perspective on the subset-subspace analogy problem . Generating function relations for the generalized binomial coefficie nts are derived by formal methods, (C) 1998 Academic Press.