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Supersymmetric gaps of a numerical semigroup with two generators

dc.contributor.authorAlmirón, Patricio
dc.contributor.authorMoyano Fernández, Julio-José
dc.date.accessioned2023-06-22T10:53:05Z
dc.date.available2023-06-22T10:53:05Z
dc.date.issued2022-04-10
dc.description.abstractIn this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf number. We prove that the set of supersymmetric and self-symmetric gaps completely determines the semigroup and we compare this set with the fundamental gaps of the semigroup.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
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/73969
dc.identifier.doi10.1080/00927872.2022.2058521
dc.identifier.issn0092-7872
dc.identifier.officialurlhttp://www.tandfonline.com/toc/lagb20/current
dc.identifier.urihttps://hdl.handle.net/20.500.14352/71835
dc.journal.titleCommunications in Algebra
dc.language.isoeng
dc.publisherTaylor & Francis
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.cdu512.74
dc.subject.keywordNumerical semigroup
dc.subject.keywordFrobenius problem
dc.subject.keywordG-semimodule
dc.subject.keywordSyzygy.
dc.subject.ucmÁlgebra
dc.subject.ucmGrupos (Matemáticas)
dc.subject.unesco1201 Álgebra
dc.titleSupersymmetric gaps of a numerical semigroup with two generators
dc.typejournal article
dcterms.referencesP. Almirón, J.J. Moyano-Fernández, A formula for the conductor of a semimodule of a numerical semigroup with two generators, Preprint, arXiv:2007.10003 (2020). 2. A. Brauer, J.E. Shockley, On a problem of Frobenius, J. reine und angewandteMath. 211 (1962), 215–220. 3. M. Delgado, Conjecture of Wilf: A survey. In: V. Barucci et al. (eds.), Numerical Semigroups, Springer INdAM Series 40, Springer Nature Switzerland, 2020. 4. R. Fr ¨oberg, C. Gottlieb, R. H¨aggkvist, On numerical semigroups, Semigroup Forum 35 (1987), 63–83. 5. E. Kunz, J. Herzog, Die Wertehalbgruppe eines lokalen Rings der Dimension 1. Sitzungsberichte der HeidelbergerAkademie derWissenschaften (Mathematische-naturwissenschaftlicheKlasse), 27–67. Springer-Verlag (1971). 6. J.J. Moyano-Fern´andez, Fractional ideals and integration with respect to the generalised Euler characteristic, Monatsh. Math. 176 (2015), 459–479. 7. J.J. Moyano-Fern´andez, J. Uliczka, Lattice paths with given number of turns and numerical semigroups, Sem.Forum 88, no. 3, (2014), 631–646. 8. J.J. Moyano-Fern´andez, J. Uliczka, Duality and syzygies for semimodules over numerical semigroups, Sem.Forum 92, no. 3, (2016), 675–690. 9. J. L. Ram´ırez Alfons´ın, The Diophantine Frobenius problem, Oxford Lecture Series in Mathematics and its Applications 30, Oxford University Press, Oxford (2005). 10. J.C. Rosales, Fundamental gaps of numerical semigroups generated by two elements, Lin. Alg. Appl. 405 (2005), 200-208. 11. J. C. Rosales, P. A. Garc´ıa Sanchez, J.I. Garc´ıa-Garc´ıa, J. A. Jim´enez Madrid, Fundamental gaps in numerical semigroups, J. Pure Appl. Alg. 189 (2004), 301–313. 12. J. C. Rosales, P. A. Garc´ıa Sanchez, Numerical Semigroups, Springer, New York (2009). 13. L. Tozzo, Poincar´e Series on Good Semigroup Ideals. In V. Barucci et al. (eds.), Numerical Semigroups, Springer INdAM Series 40, Springer Nature Switzerland AG (2020). 14. H. Wilf, A circle-of-lights algorithm for the money-changing problem, Amer. Math. Monthly 85 (1978) 562–565.
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