Partition identities associated with $A_r$-Surface singularities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917207587422208 |
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| author | Afsharijoo, Pooneh Pérez, Pedro D. González Mourtada, Hussein |
| author_facet | Afsharijoo, Pooneh Pérez, Pedro D. González Mourtada, Hussein |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partition identities associated with $A_r$-Surface singularities Afsharijoo, Pooneh Pérez, Pedro D. González Mourtada, Hussein Algebraic Geometry Commutative Algebra Combinatorics 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. |
| title | Partition identities associated with $A_r$-Surface singularities |
| topic | Algebraic Geometry Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2601.12048 |