On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912849920524288 |
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| author | Kumar, Rahul Punia, Nargish |
| author_facet | Kumar, Rahul Punia, Nargish |
| contents | In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities connecting these various classes of partitions. Moreover, our identities help us to extend the Euler's partition theorem. An analogue of Legendre's theorem of the partition-theoretic interpretation of Euler's pentagonal number theorem is also derived. Both combinatorial and $q$-series proofs are given for our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts Kumar, Rahul Punia, Nargish Combinatorics Number Theory In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities connecting these various classes of partitions. Moreover, our identities help us to extend the Euler's partition theorem. An analogue of Legendre's theorem of the partition-theoretic interpretation of Euler's pentagonal number theorem is also derived. Both combinatorial and $q$-series proofs are given for our results. |
| title | On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2601.18657 |