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arXiv · 2107.06793

Multiplication theorems for self-conjugate partitions

David Wahiche
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Abstract

In 2011, Han and Ji proved addition-multiplication theorems for integer partitions, from which they derived modular analogues of many classical identities involving hook-length. In the present paper, we prove addition-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. This gives us as consequences many self-conjugate modular versions of classical hook-lengths identities for partitions. Our tools are mainly based on fine properties of the Littlewood decomposition restricted to self-conjugate partitions.

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BibTeXRIS

David Wahiche. 2021-07-14. Multiplication theorems for self-conjugate partitions. https://doi.org/10.5070/c62257879

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