A Decomposition of Cylindric Partitions and Cylindric Partitions into Distinct Parts

Kağan Kurşungöz, Halime Ömrüuzun Seyrek

Published 2023-08-28Version 1

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. With due computational support; the other part of Corteel, Dousse, and Uncu's conjecture, which also appeared in Warnaar's work, is extended. The approaches and proofs are elementary and combinatorial.