@misc{10481/49801,
year = {2016},
month = {6},
url = {http://hdl.handle.net/10481/49801},
abstract = {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.},
organization = {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.},
publisher = {Walter de Gruyter GmbH},
keywords = {Diophantine inequalities},
keywords = {Submonoids},
keywords = {Numerical semigroups},
keywords = {Non-homogeneous patterns},
keywords = {Frobenius varieties},
keywords = {Trees},
keywords = {Profitable transport},
title = {Numerical semigroups in a problem about cost-effective transport},
doi = {10.1515/forum-2015-0123},
author = {Robles-Pérez, Aureliano M. and Rosales González, José Carlos},
}