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Partitions into parts simultaneously regular, distinct, and/or flat

Research paper by William J. Keith

Indexed on: 13 Nov '19Published on: 12 Nov '19Published in: arXiv - Mathematics - Combinatorics



Abstract

We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by $m$, appearing fewer than $m$ times, or differing by less than $m$. We find results on their behavior and generating functions: more results for those simultaneously regular and distinct, fewest for those distinct and flat. We offer some conjectures in the area.