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A refinement of and a companion to MacMahon's partition identity (2307.16753v1)
Published 31 Jul 2023 in math.CO and math.NT
Abstract: We provide a refinement of MacMahon's partition identity on sequence-avoiding partitions, and use it to produce another mod 6 partition identity. In addition, we show that our technique also extends to cover Andrews's generalization of MacMahon's identity. Our proofs are bijective in nature, exploiting a theorem of Xiong and Keith.
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