Abstract:We consider the number of the 6-regular partitions of n, b6(n), and give infinite families of congruences modulo 3 (in arithmetic progression) for b6(n). We also consider the number of the partitions of n into distinct parts not congruent to ±2 modulo 6, Q2(n), and investigate connections between b6(n) and Q2(n) providing new combinatorial interpretations for these partition functions. In this context, we discover new infinite families of linear inequalities involving Euler's partition function p(n). Infinite … Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.