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arXiv · 1809.02685

Marking and shifting a part in partition theorems

Kathleen O'Hara·Dennis Stanton
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Abstract

Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identities, Euler's odd=distinct theorem, and the Andrews-Gordon identities. Generalizations of each of these theorems are given where a single part is "marked" or weighted. This allows a single part to be replaced by a new larger part, "shifting" a part, and analogous combinatorial results are given in each case. Versions are also given for marking a sum of parts.

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Kathleen O'Hara, Dennis Stanton. 2018-09-07. Marking and shifting a part in partition theorems. https://arxiv.org/abs/1809.02685

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