Numerical semigroups in a problem about cost-effective transport
Robles-Pérez, Aureliano M.
Rosales González, José Carlos
Diophantine inequalities
Submonoids
Numerical semigroups
Non-homogeneous patterns
Frobenius varieties
Trees
Profitable transport
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.
2018-03-05T08:21:51Z
2018-03-05T08:21:51Z
2016-06-14
info:eu-repo/semantics/article
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]
0933-7741
1435-5337
http://hdl.handle.net/10481/49801
10.1515/forum-2015-0123
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/
info:eu-repo/semantics/openAccess
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Walter de Gruyter GmbH