On partitions with bounded largest part and fixed integral GBG-rank modulo primes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918007714873344 |
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| author | Berkovich, Alexander Dhar, Aritram |
| author_facet | Berkovich, Alexander Dhar, Aritram |
| contents | In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo $t$ which is a generalization of the well-known BG-rank. In this paper, we use the Littlewood decomposition of partitions to study partitions with bounded largest part and fixed integral value of GBG-rank modulo primes. As a consequence, we obtain new elegant generating function formulas for unrestricted partitions, self-conjugate partitions, and partitions whose parts repeat a finite number of times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15117 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On partitions with bounded largest part and fixed integral GBG-rank modulo primes Berkovich, Alexander Dhar, Aritram Number Theory Combinatorics 05A15, 05A17, 05A19, 11P81, 11P83, 11P84 In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo $t$ which is a generalization of the well-known BG-rank. In this paper, we use the Littlewood decomposition of partitions to study partitions with bounded largest part and fixed integral value of GBG-rank modulo primes. As a consequence, we obtain new elegant generating function formulas for unrestricted partitions, self-conjugate partitions, and partitions whose parts repeat a finite number of times. |
| title | On partitions with bounded largest part and fixed integral GBG-rank modulo primes |
| topic | Number Theory Combinatorics 05A15, 05A17, 05A19, 11P81, 11P83, 11P84 |
| url | https://arxiv.org/abs/2312.15117 |