Séminaire Lotharingien de Combinatoire, 86B.64 (2022), 12 pp.
David Wahiche
Multiplication Theorems for Self-Conjugate Partitions
Abstract.
In 2011, Han and Ji proved, by using fine properties of the Littlewood decomposition, multiplication theorems for integer partitions. From the latter, they derived modular analogues of many classical identities involving hook-length. In the present paper, we prove multiplication theorems for the subset of self-conjugate partitions. Although difficulties arise due to parity questions, we are almost always able to include the BG-rank introduced by Berkovich and Garvan.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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