Congruences modulo powers of $5$ for odd ranks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910570000678912 |
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| author | Mao, Renrong Zhou, Zhiqian |
| author_facet | Mao, Renrong Zhou, Zhiqian |
| contents | In 2007, Andrews studied the odd Durfee symbols and their odd ranks. Let $N^0(m,k,n)$ denote the number of odd Durfee symbols of $n$ with odd rank congruent to $m$ modulo $k$. Motivated by Andrews' work, many authors obtained generating functions of $N^0(m,k,n)$ from which relations between odd ranks are proved. In this paper, we establish a family of congruences for odd ranks modulo powers of $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Congruences modulo powers of $5$ for odd ranks Mao, Renrong Zhou, Zhiqian Combinatorics In 2007, Andrews studied the odd Durfee symbols and their odd ranks. Let $N^0(m,k,n)$ denote the number of odd Durfee symbols of $n$ with odd rank congruent to $m$ modulo $k$. Motivated by Andrews' work, many authors obtained generating functions of $N^0(m,k,n)$ from which relations between odd ranks are proved. In this paper, we establish a family of congruences for odd ranks modulo powers of $5$. |
| title | Congruences modulo powers of $5$ for odd ranks |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.09628 |