The Frobenius problem for Numerical Semigroups generated by binomial coefficients
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918153394585600 |
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| author | Hwang, WonTae Song, Kyunghwan |
| author_facet | Hwang, WonTae Song, Kyunghwan |
| contents | The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$, and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for the numerical semigroups generated by binomial coefficients. As applications, we provide some nontrivial identities among binomial coefficients, and we also connect the main results to the theory of $(s,s+1,s+p)$-core partitions of integers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Frobenius problem for Numerical Semigroups generated by binomial coefficients Hwang, WonTae Song, Kyunghwan Number Theory Primary 11A67, 11A07, 11B65, 05A10, 05A17 The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$, and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for the numerical semigroups generated by binomial coefficients. As applications, we provide some nontrivial identities among binomial coefficients, and we also connect the main results to the theory of $(s,s+1,s+p)$-core partitions of integers. |
| title | The Frobenius problem for Numerical Semigroups generated by binomial coefficients |
| topic | Number Theory Primary 11A67, 11A07, 11B65, 05A10, 05A17 |
| url | https://arxiv.org/abs/2412.17882 |