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Linked partition ideals and the Alladi--Schur theorem

2021/10/25 by George E. Andrews, Andrews, George E., Shane Chern +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2110.13247

Abstract

Let \mathscrS denote the set of integer partitions into parts that differ by at least 3, with the added constraint that no two consecutive multiples of 3 occur as parts. We derive trivariate generating functions of Andrews--Gordon type for partitions in \mathscrS with both the number of parts and the number of even parts counted. In particular, we provide an analytic counterpart of Andrews' recent refinement of the Alladi--Schur theorem.

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