Kunz, E. (2016) On the type of certain numerical semigroups and a question of Wilf. SEMIGROUP FORUM, 93 (1). pp. 205-210. ISSN 0037-1912, 1432-2137
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Let H be a numerical semigroup with embedding dimension , type t(H), conductor c(H) and genus g(H). Wilf's question (Am Math Mon 25:562-565, 1978) asks wether edim(H) . (c(H) - g(H)) - c(H) >= 0 for all numerical semigroups H. Positive answers in special cases have been given in Bras-Amoros (Semigroup Forum 76:379-384, 2008), Dobbs and Matthews (Focus on Commutative Rings Research, 2006), Froberg et al. (Semigroup Forum 35:63-83, 1987), Kaplan (J. Pure Appl. Algebra 26:1016-1032 , 2012), and recently in Moscariello and Sammartano (Math Z 280:47-53, 2015). In Froberg et al. Theorem 20 it was proved that the formula (t(H) + 1) . (c(H) - g(H)) - c(H) >= 0 always holds true. Using the geometrical illustration of numerical semigroups from Kunz and Waldi (Semigroup Forum 89:664-691, 2014) it will be shown that or even for certain explicitly given collections of numerical semigroups H, which implies a positive answer to Wilf's question for these semigroups.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NODAL CURVES; GENUS; Numerical semigroup; Geometrical illustration; Type; Wilf's question |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Apr 2019 07:07 |
| Last Modified: | 08 Apr 2019 07:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3573 |
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