A decomposition of cylindric partitions and cylindric partitions into distinct parts

Abstract

We introduce the notion of pivot in a chain of skew diagrams in the context of cylindric partitions. Then, we show that cylindric partitions are in one-to-one correspondence with a pair consisting of an ordinary partition and a suitably restricted chain of pivots. Next, we show the general form of the generating function for cylindric partitions into distinct parts and give some examples. We prove part of a conjecture by Corteel, Dousse, and Uncu. The approaches and proofs are elementary and combinatorial.