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

2016/07/31 by Berkovich, Alexander, Uncu, Ali Kemal
#05A15 #05A17 #05A19 #11B34 #11B75 #11P81 #11P84 #33D15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.00193

Abstract

We use the q-binomial theorem, the q-Gauss sum, and the ₂ϕ₁ → ₂ϕ₂ 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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