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arXiv · 2106.09773

New infinite hierarchies of polynomial identities related to the Capparelli partition theorems

Alexander Berkovich·Ali Kemal Uncu
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Abstract

We prove a new polynomial refinement of the Capparelli's identities. Using a special case of Bailey's lemma we prove many infinite families of sum-product identities that root from our finite analogues of Capparelli's identities. We also discuss the $q\mapsto 1/q$ duality transformation of the base identities and some related partition theoretic relations.

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Alexander Berkovich, Ali Kemal Uncu. 2021-06-17. New infinite hierarchies of polynomial identities related to the Capparelli partition theorems. https://arxiv.org/abs/2106.09773

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