SIP classes and four-parameter partition identities
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917308699508736 |
|---|---|
| author | Li, Runqiao |
| author_facet | Li, Runqiao |
| contents | The four-parameter weight of partitions played an important role in the theory of integer partitions, for its connection with various statistics, including the alternating sum and the BG-rank. In 2022, Andrews introduced the SIP classes, by which he reviewed a number of classic partition identities and provided new combinatorial insights. In this work, we extend the SIP classes and provide a unified method to study the four-parameter weight of partitions. By treating partitions with position parity as examples, we provide four-parameter partition identities related to these partition sets. And as corollary, we also present the generating functions that keep track of the BG-rank and the joint distribution of the number of odd parts and the alternating sum, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SIP classes and four-parameter partition identities Li, Runqiao Combinatorics Number Theory 05A17, 11P84, 11P82 The four-parameter weight of partitions played an important role in the theory of integer partitions, for its connection with various statistics, including the alternating sum and the BG-rank. In 2022, Andrews introduced the SIP classes, by which he reviewed a number of classic partition identities and provided new combinatorial insights. In this work, we extend the SIP classes and provide a unified method to study the four-parameter weight of partitions. By treating partitions with position parity as examples, we provide four-parameter partition identities related to these partition sets. And as corollary, we also present the generating functions that keep track of the BG-rank and the joint distribution of the number of odd parts and the alternating sum, respectively. |
| title | SIP classes and four-parameter partition identities |
| topic | Combinatorics Number Theory 05A17, 11P84, 11P82 |
| url | https://arxiv.org/abs/2603.02575 |