Arithmetic Properties of Overcolored Odd Partitions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913149959012352 |
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| author | Thejitha, M. P. Fathima, S. N. |
| author_facet | Thejitha, M. P. Fathima, S. N. |
| contents | Let $\bar{a}_s(n)$ denote the number of partitions of $n$, wherein each odd part is multicolored (atmost $s\ge 1$ colors) and the first appearance of parts may be overlined. In this paper, we establish new families of congruences modulo powers of $2$ satisfied by $\bar{a}_s(n)$ for infinitely many $s$. Our approach builds upon generating function manipulations, Hecke eigenform theory and results of Newman. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21321 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arithmetic Properties of Overcolored Odd Partitions Thejitha, M. P. Fathima, S. N. Number Theory 05A17, 11P83 Let $\bar{a}_s(n)$ denote the number of partitions of $n$, wherein each odd part is multicolored (atmost $s\ge 1$ colors) and the first appearance of parts may be overlined. In this paper, we establish new families of congruences modulo powers of $2$ satisfied by $\bar{a}_s(n)$ for infinitely many $s$. Our approach builds upon generating function manipulations, Hecke eigenform theory and results of Newman. |
| title | Arithmetic Properties of Overcolored Odd Partitions |
| topic | Number Theory 05A17, 11P83 |
| url | https://arxiv.org/abs/2605.21321 |