Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912378003652608 |
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| author | Amdeberhan, Tewodros Sellers, James A. Singh, Ajit |
| author_facet | Amdeberhan, Tewodros Sellers, James A. Singh, Ajit |
| contents | A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime Amdeberhan, Tewodros Sellers, James A. Singh, Ajit Number Theory Combinatorics A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions. |
| title | Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2407.00058 |