Wilf's conjecture in fixed multiplicity
Autor(en): | Bruns, Winfried Garcia-Sanchez, Pedro O'Neill, Christopher Wilburne, Dane |
Stichwörter: | Kunz polyhedron; Mathematics; Numerical semigroup; Wilf's conjecture | Erscheinungsdatum: | 2020 | Herausgeber: | WORLD SCIENTIFIC PUBL CO PTE LTD | Journal: | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | Volumen: | 30 | Ausgabe: | 4 | Startseite: | 861 | Seitenende: | 882 | Zusammenfassung: | We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity m, and use it to prove Wilf's conjecture holds whenever m <= 18. Our algorithm utilizes techniques from polyhedral geometry, and includes a parallelizable algorithm for enumerating the faces of any polyhedral cone up to orbits of an automorphism group. We also introduce a new method of verifying Wilf's conjecture via a combinatorially flavored game played on the elements of a certain finite poset. |
ISSN: | 02181967 | DOI: | 10.1142/S021819672050023X |
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