Enumeration of partitions via socle reduction
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916569787924480 |
|---|---|
| author | Graffeo, Michele Monavari, Sergej Moschetti, Riccardo Ricolfi, Andrea T. |
| author_facet | Graffeo, Michele Monavari, Sergej Moschetti, Riccardo Ricolfi, Andrea T. |
| contents | We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional partitions, satisfying suitable constraints on their embedding dimension and socle type. We provide exact formulas for the generating functions of several infinite families of such partitions, and design a procedure enumerating them in the general case. As a proof of concept, we determine the number of partitions of size up to 30 in any dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of partitions via socle reduction Graffeo, Michele Monavari, Sergej Moschetti, Riccardo Ricolfi, Andrea T. Combinatorics Commutative Algebra Algebraic Geometry 05A15, 05A17 We study the enumeration problem of higher dimensional partitions, a natural generalisation of classical integer partitions. We show that their counting problem is equivalent to the enumeration of simpler classes of higher dimensional partitions, satisfying suitable constraints on their embedding dimension and socle type. We provide exact formulas for the generating functions of several infinite families of such partitions, and design a procedure enumerating them in the general case. As a proof of concept, we determine the number of partitions of size up to 30 in any dimension. |
| title | Enumeration of partitions via socle reduction |
| topic | Combinatorics Commutative Algebra Algebraic Geometry 05A15, 05A17 |
| url | https://arxiv.org/abs/2501.10267 |