RT Journal Article
T1 Supersymmetric gaps of a numerical semigroup with two generators
A1 Almirón, Patricio
A1 Moyano Fernández, Julio-José
AB In 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.
PB Taylor & Francis
SN 0092-7872
YR 2022
FD 2022-04-10
LK https://hdl.handle.net/20.500.14352/71835
UL https://hdl.handle.net/20.500.14352/71835
LA eng
NO P. 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 HeidelbergerAkademiederWissenschaften (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.
NO Ministerio de Ciencia e Innovación (MICINN)
NO Universitat Jaume I
DS Docta Complutense
RD 28 abr 2024