Factors of Some Lacunary q-Binomial Sums

Abstract

In this paper, we prove a divisibility result for the lacunary $q$-binomial sum $$ \sum_{k\equiv r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}. $$

References in corpus (1)

• A generalization of the Gaussian formula and a q-analog of Fleck's congruence

Cited by in corpus (2)

• Congruences for $q$-binomial coefficients
• An inductive proof of Straub's q-analogue of Ljunggren's congruence