Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908569240076288 |
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| author | Sriram, S. Christopher, A. David |
| author_facet | Sriram, S. Christopher, A. David |
| contents | Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $τ_k(n)$, is defined as follows: \[q\prod_{m=1}^{\infty}(1-q^m)^k=\sum_{n=1}^{\infty}τ_k(n)q^n, \] where $k$ is an integer. We express $τ_k(n)$ as a binomial coefficient weighted partition sum. Consequently, we obtain congruence identities that relate $τ_k(n)$, $R_t(n)$ and partition function weighted composition sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums Sriram, S. Christopher, A. David Number Theory Let $n$ and $t$ be positive integers with $t\geq 2$. Let $R_t(n)$ be the number of $t$-regular partitions of $n$. A class of functions, denoted $τ_k(n)$, is defined as follows: \[q\prod_{m=1}^{\infty}(1-q^m)^k=\sum_{n=1}^{\infty}τ_k(n)q^n, \] where $k$ is an integer. We express $τ_k(n)$ as a binomial coefficient weighted partition sum. Consequently, we obtain congruence identities that relate $τ_k(n)$, $R_t(n)$ and partition function weighted composition sums. |
| title | Congruences Relating Regular Partition Functions, a Genearalised Tau Function and Partition Function Weighted Composition Sums |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.26559 |