A combinatorial problem and numerical semigroups

Aureliano M. Robles Pérez, José Carlos Rosales

Abstract


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:

  1. The cardinality of C is equal to g;

  2. If x, y ∈ ℕ \ {0} and x + y ∈ C, then C ∩ {x, y} ≠ ∅;

  3. If x ∈ C and (x − bi) / ai ∈ ℕ \ {0} for some i ∈ {1, …, n}, then (x − bi) / ai ∈ C;

  4. X ∩ C = ∅.


Keywords


Combinatorial problems, numerical semigroups, Frobenius varieties, Frobenius pseudo-varieties

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DOI: https://doi.org/10.26493/1855-3974.989.d15

ISSN: 1855-3974

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