Linear identities for partition pairs with $5$-cores
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915732134035456 |
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| author | Guadalupe, Russelle |
| author_facet | Guadalupe, Russelle |
| contents | We prove an infinite family of linear identities for the number $A_5(n)$ of partition pairs of $n$ with $5$-cores by using certain theta function identities involving the Ramanujan's parameter $k(q)$ due to Cooper, and Lee and Park. Consequently, we deduce an infinite family of congruences for $A_5(n)$ using these linear identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04743 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear identities for partition pairs with $5$-cores Guadalupe, Russelle Number Theory Combinatorics 11P83, 05A17, 11F27 We prove an infinite family of linear identities for the number $A_5(n)$ of partition pairs of $n$ with $5$-cores by using certain theta function identities involving the Ramanujan's parameter $k(q)$ due to Cooper, and Lee and Park. Consequently, we deduce an infinite family of congruences for $A_5(n)$ using these linear identities. |
| title | Linear identities for partition pairs with $5$-cores |
| topic | Number Theory Combinatorics 11P83, 05A17, 11F27 |
| url | https://arxiv.org/abs/2601.04743 |