Wilf's question in numerical semigroups $S_3$ revisited and inequalities for rescaled genera
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910873314918400 |
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| author | Fel, Leonid G. |
| author_facet | Fel, Leonid G. |
| contents | We consider numerical semigroups $S_3 = \langle d_1,d_2,d_3\rangle$, minimally generated by three positive integers. We revisit the Wilf question in $S_3$ and, making use of identities for degrees of syzygies of such semigroups, give a short proof of existence of an affirmative answer. We find also the lower bound for Frobenius numbers of $S_3$ and upper and lower bounds for rescaled genera. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wilf's question in numerical semigroups $S_3$ revisited and inequalities for rescaled genera Fel, Leonid G. Commutative Algebra Primary - 20M14, Secondary - 11P81 We consider numerical semigroups $S_3 = \langle d_1,d_2,d_3\rangle$, minimally generated by three positive integers. We revisit the Wilf question in $S_3$ and, making use of identities for degrees of syzygies of such semigroups, give a short proof of existence of an affirmative answer. We find also the lower bound for Frobenius numbers of $S_3$ and upper and lower bounds for rescaled genera. |
| title | Wilf's question in numerical semigroups $S_3$ revisited and inequalities for rescaled genera |
| topic | Commutative Algebra Primary - 20M14, Secondary - 11P81 |
| url | https://arxiv.org/abs/2406.13580 |