Neighborly partitions and the numerators of Rogers-Ramanujan identities

Published 7 Jan 2022 in math.CO and math.AC | (2201.02481v1)

Abstract: We prove two partition identities which are dual to the Rogers-Ramanujan identities. These identities are inspired by (and proved using) a correspondence between three kinds of objects: a new type of partitions (neighborly partitions), monomial ideals and some infinite graphs.

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