Geodesic
A combinatorial problem and numerical semigroups
Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 323-336.

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Let a = (a1, …, an) and b = (b1, …, bn) be two n-tuples of positive integers, let X be a set of positive integers, and let g be a positive integer. In this work we show an algorithmic process in order to compute all the sets C of positive integers that fulfill the following conditions:The cardinality of C is equal to g;If x, y ∈ ℕ \ {0} and x + y ∈ C, then C ∩ {x, y} ≠ ∅;If x ∈ C and (x − bi) / ai ∈ ℕ \ {0} for some i ∈ {1, …, n}, then (x − bi) / ai ∈ C;X ∩ C = ∅.
DOI : 10.26493/1855-3974.989.d15
Keywords: Combinatorial problems, numerical semigroups, Frobenius varieties, Frobenius pseudo-varieties 
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Aureliano M. Robles Pérez; José Carlos Rosales. A combinatorial problem and numerical semigroups. Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 323-336. doi : 10.26493/1855-3974.989.d15. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.989.d15/

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