On divisor-closed submonoids and minimal distances in finitely generated monoids. (July 2019)

• Record Type: Journal Article
• Authors: García-García, J.I.; Marín-Aragón, D.; Moreno-Frías, M.A.
• Is Part Of: Journal of symbolic computation. Volume 93(2019)
• Page Start: 230
• Page End: 245
• Publication Date: 2019-07
• Subjects: 13A05 -- 11R27 -- 20M14 -- 20M13 -- 52B11; Divisor-closed submonoid -- Archimedean component -- Set of minimal distances -- Non-unique factorizations -- Commutative monoid -- Cancellative monoid -- Polyhedral cone -- Finitely generated monoid; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.008
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study the lattice of divisor-closed submonoids of finitely generated cancellative commutative monoids. In case the monoid is an affine semigroup, we give a geometrical characterization of such submonoids in terms of its cone. Finally, we use our results to give an algorithm for computing Δ ⁎ ( H ), the set of minimal distances of H .