A Decomposition of Cylindric Partitions and Cylindric Partitions into Distinct Parts

Abstract

We show that cylindric partitions are in one-to-one correspondence with a pair which has an ordinary partition and a colored partition into distinct parts. Then, 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.

Second version. Many inaccuracies are corrected thanks to Ole Warnaar. 44 pages, 50+ figures