Congruences for restricted plane overpartitions modulo 4 and 8

Abstract

In 2009, Corteel, Savelief and Vuletić generalized the concept of overpartitions to a new object called plane overpartitions. In recent work, the author considered a restricted form of plane overpartitions called k-rowed plane overpartions and proved a method to obtain congruences for these and other types of combinatorial generating functions. In this paper, we prove several restricted and unrestricted plane overpartition congruences modulo 4 and 8 using other techniques.2010 Mathematics Subject Classification. 11P83.

2-Rowed Plane Overpartitions Modulo 8 and 16

“…In [5], various identities modulo 4 and 8 for restricted plane overpartitions were established and proved. Congruences modulo 4 between overpartitions and plane overpartitions have also been demonstrated.…”