Neighborly partitions and the numerators of Rogers-Ramanujan identities

2022/01/07 by Zahraa Mohsen, Mohsen, Zahraa, Hussein Mourtada +1 · 1 citation
Computer Science · Mathematics · #05A17 #05A19 #05C31 #11P81 #11P84 #13D40 #13F55 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Computational Drug Discovery Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2201.02481

openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On the Göllnitz-Gordon-Andrews identities via commutative algebra

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• Notes for Neighborly Partitions
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