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arXiv · 2601.12048

Partition identities associated with $A_r$-Surface singularities

Pooneh Afsharijoo·Pedro D. González Pérez·Hussein Mourtada
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Abstract

We prove a family of partition identities involving integer partitions in three colors. The conditions imposed on the types of partitions appearing in these identities involve constraints that arise in the Rogers-Ramanujan and Andrews-Gordon identities, as well as in their recent extensions. The identities established in this paper are associated with the $A_r$ surface singularities via the arc HP-series, which provides a measure of singularities of algebraic varieties defined using arc spaces.

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Pooneh Afsharijoo, Pedro D. González Pérez, Hussein Mourtada. 2026-01-17. Partition identities associated with $A_r$-Surface singularities. https://arxiv.org/abs/2601.12048

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