Partition identities associated with $A_r$-Surface singularities
Algebraic Geometry
2026-01-21 v1 Commutative Algebra
Combinatorics
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 surface singularities via the arc HP-series, which provides a measure of singularities of algebraic varieties defined using arc spaces.
Cite
@article{arxiv.2601.12048,
title = {Partition identities associated with $A_r$-Surface singularities},
author = {Pooneh Afsharijoo and Pedro D. González Pérez and Hussein Mourtada},
journal= {arXiv preprint arXiv:2601.12048},
year = {2026}
}