Eliahou number, Wilf function and concentration of a numerical semigroup

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dc.contributor.authorAlmirón, Patricio
dc.contributor.authorMoyano Fernández, Julio-José
dc.date.accessioned2023-06-22T10:53:01Z
dc.date.available2023-06-22T10:53:01Z
dc.date.issued2022-03-30
dc.description.abstractWe give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have a negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new examples of numerical semigroups with a negative Eliahou number satisfying the Wilf conjecture. In addition, we introduce the notion of highly dense numerical semigroup; this yields a new family of numerical semigroups satisfying the Wilf conjecture. Moreover, we use the Wilf function of a numerical semigroup to prove that the Eliahou number of a highly dense numerical semigroup is positive under certain additional hypothesis. These results provide new evidences in favour of the Wilf conjecture.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipUniversitat Jaume I
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/73967
dc.identifier.doi10.2989/16073606.2022.2041126
dc.identifier.issn1607-3606
dc.identifier.officialurlhttps://doi.org/10.2989/16073606.2022.2041126
dc.identifier.urihttps://hdl.handle.net/20.500.14352/71833
dc.journal.titleQuaestiones Mathematicae
dc.language.isospa
dc.publisherNational Inquiry Services Centre (NISC)
dc.relation.projectIDMTM2016- 76868-C2-1-P; PGC2018-096446-B-C22
dc.relation.projectIDUJI-B2018-10
dc.rights.accessRightsopen access
dc.subject.cdu512
dc.subject.cdu512.53
dc.subject.keywordNumerical semigroup
dc.subject.keywordCoin change problem
dc.subject.keywordWilf conjecture
dc.subject.keywordEliahou number
dc.subject.keywordConcentration.
dc.subject.ucmÁlgebra
dc.subject.ucmGrupos (Matemáticas)
dc.subject.unesco1201 Álgebra
dc.titleEliahou number, Wilf function and concentration of a numerical semigroup
dc.typejournal article
dcterms.references1. P. Almirón, J.J. Moyano-Fernández, A new perspective on the Wilf conjecture on numerical semigroups, arXiv: 2012.01358 (2020). 2. R. Apéry, Sur les branches superlinéaires des courbes algébriques, C.R. Acad. Sci. Paris 222 (1946), 1198– 1200. 3. M. Delgado, On a question of Eliahou and a conjecture of Wilf, Math. Z. 288(1-2) (2018) 595–627. 4. M. Delgado, Conjecture ofWilf: A survey. In: V. Barucci et al. (eds.), Numerical Semigroups, 39–62, Springer INdAM Series 40, Springer Nature Switzerland, 2020. 5. M. Delgado, Trimming the numerical semigroups tree to probe Wilf’s conjecture to higher genus, arXiv:1910.12377. 6. M. Delgado, P. A. Garcia-Sanchez, J. Morais, NumericalSgps, a package for numerical semigroups, Version 1.1.11. https://gap-packages.github.io/numericalsgps,Mar 2019. Refereed GAP package. 7. D.E. Dobbs, G.L. Matthews, On a question of Wilf concerning numerical semigroups. In: Focus on Commu- tative Rings Research, 193–202, Nova Sci. Publ., New York, 2006. 8. S. Eliahou,Wilf’s conjecture and Macaulay’s theorem, J. Eur. Math. Soc. (JEMS) 20 (9) (2018) 2105–2129. 9. S. Eliahou, J. Fromentin, Near-misses in Wilf’s conjecture, Semigroup Forum 98(2) (2019) 285–298. 10. R. Fröberg, C. Gottlieb, R. H¨aggkvist, On numerical semigroups, Semigroup Forum 35 (1987) 63–83. 11. J. Fromentin, F. Hivert, Exploring the tree of numerical semigroups,Math. Comput. 85 (2016) 2553–2568. 12. GAP – Groups, Algorithms, and Programming, Version 4.10.0. https://www.gap-system.org, Nov 2018. 13. N. Kaplan, Counting numerical semigroups by genus and some cases of a question of Wilf, Journal of Pure and Applied Algebra, 216 (2012) 1016–1032. 14. E. Kunz, J. Herzog, Die Wertehalbgruppe eines lokalen Rings der Dimension 1. Sitzungsberichte der HeidelbergerAkademie derWissenschaften (Mathematische-naturwissenschaftlicheKlasse), 27–67. Springer-Verlag (1971). 15. A. Moscariello, A. Sammartano, On a conjecture by Wilf about the Frobenius number, Math. Z. 280(1-2) (2015) 47–53. 16. J.L. Ramírez Alfonsín, The Diophantine Frobenius problem, Oxford Lecture Series in Mathematics and its Applications 30, Oxford University Press, Oxford (2005). 17. J.C. Rosales, M.B. Branco, M.A. Traesel, Numerical semigroups with concentration two, Preprint arXiv:2103.16723. 18. J.C. Rosales, P. A. García Sanchez, Numerical Semigroups, Springer (2009). 19. A. Sammartano, Numerical semigroupswith large embedding dimension satisfyWilf’s conjecture, Semigroup Forum 85 (2012) 439–447. 20. H. Wilf, A circle-of-lights algorithm for the money-changing problem, Amer. Math. Monthly 85 (1978) 562– 565
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