New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions

Alexander Berkovich; Ali Kemal Uncu

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arXiv · 1608.00193

New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions

Alexander Berkovich·Ali Kemal Uncu

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Abstract

We use the $q$-binomial theorem, the $q$-Gauss sum, and the ${}_2\phi_1 \rightarrow {}_2\phi_2$ transformation of Jackson to discover and prove many new weighted partition identities. These identities involve unrestricted partitions, overpartitions, and partitions with distinct even parts. Smallest part of the partitions plays an important role in our analysis. This work was motivated in part by the research of Krishna Alladi.

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Alexander Berkovich, Ali Kemal Uncu. 2016-07-31. New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions. https://arxiv.org/abs/1608.00193

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