Numerical semigroups in a problem about cost-effective transport
Metadatos
Afficher la notice complèteEditorial
Walter de Gruyter GmbH
Materia
Diophantine inequalities Submonoids Numerical semigroups Non-homogeneous patterns Frobenius varieties Trees Profitable transport
Date
2016-06-14Referencia bibliográfica
Robles-Pérez, A.M.; Rosales González, J.C. Numerical semigroups in a problem about cost-effective transport. Forum Mathematicum, 29(2): 329-345 (2016). [http://hdl.handle.net/10481/49801]
Patrocinador
Both authors are supported by the project MTM2014-55367-P, which is funded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER, and by the Junta de Andalucía Grant Number FQM-343. The second author is also partially supported by Junta de Andalucía/Feder Grant Number FQM-5849.Résumé
Let N be the set of nonnegative integers. A problem about how to transport profitably an organized group of persons leads us to study the set T formed by the integers n such that the system of inequalities, with nonnegative integer coefficients, a_1x_1+⋯+a_px_p<n<b_1x_1+⋯+b_px_p
has at least one solution in N^p. We will see that T∪{0} is a numerical semigroup. Moreover, we will show that a numerical semigroup S can be obtained in this way if and only if {a+b−1,a+b+1}⊆S, for all a,b∈S∖{0}. In addition, we will demonstrate that such numerical semigroups form a Frobenius variety and we will study this variety. Finally, we show an algorithmic process in order to compute T.