Dominance Orders, Generalized Binomial Coefficients, and Kummer’s Theorem

摘要

We discuss the connections between a family of partial orders known as b-dominance orders, arithmetic in base b, and generalized binomial coefficients. In particular, we investigate theorems of Lucas and Kummer in relation to these orders and attempt to extend and explain these theorems using a family of generalized binomial coefficients derived from a simple integer sequence.