An iterative-bijective approach to asymmetric generalizations of Schur's theorem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914070411608064 |
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| author | Velenik, Laure |
| author_facet | Velenik, Laure |
| contents | In this paper, we present a new Rogers--Ramanujan type identity for overpartitions by extending the asymmetrical version of Schur's theorem due to Lovejoy to a broader class of infinite products. More precisely, we provide a combinatorial interpretation of the following product, for any positive integer $k$, as a generating function for a class of overpartitions in which parts appear in $2^k - 1$ colors: \[ \frac{(-y_1 q;q)_\infty \cdots (-y_k q;q)_\infty}{(y_1 d q;q)_\infty}. \] Our proof is bijective and unifies two earlier approaches: Lovejoy's bijective proof of the asymmetrical Schur theorem and the iterative-bijective technique developed by Corteel and Lovejoy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00846 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An iterative-bijective approach to asymmetric generalizations of Schur's theorem Velenik, Laure Combinatorics Number Theory In this paper, we present a new Rogers--Ramanujan type identity for overpartitions by extending the asymmetrical version of Schur's theorem due to Lovejoy to a broader class of infinite products. More precisely, we provide a combinatorial interpretation of the following product, for any positive integer $k$, as a generating function for a class of overpartitions in which parts appear in $2^k - 1$ colors: \[ \frac{(-y_1 q;q)_\infty \cdots (-y_k q;q)_\infty}{(y_1 d q;q)_\infty}. \] Our proof is bijective and unifies two earlier approaches: Lovejoy's bijective proof of the asymmetrical Schur theorem and the iterative-bijective technique developed by Corteel and Lovejoy. |
| title | An iterative-bijective approach to asymmetric generalizations of Schur's theorem |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2510.00846 |