On b-ary binomial coefficients with negative entries

Abstract

We extend the b-ary binomial coefficients by allowing negative entries, which is based on the generating function obtained in previous work. Besides an explicit expression for these coefficients involving restricted partition, several properties such as symmetry, congruence, Pascal-like recurrences and Chu-Vandermonde identities are presented. Finally, we also provide two other generalizations that partially satisfy Pascal-like recurrences.