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Linked partition ideals and the Alladi--Schur theorem

25 Oct 2021arXiv:2110.13247links table onlyarchive 2025-07-28

George E. Andrews, Shane Chern, Zhitai Li

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Let 𝒮 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 𝒮 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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