Algorithms for generalized numerical semigroups

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Cisto, C (Author) Other; delgado, m (Author) FCUP; Garcia Sanchez, PA (Author) Other

Journal

Title: Journal of Algebra and its Applications

Vol. 20

ISSN: 0219-4988

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 4 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-00R-XWD

DOI: 10.1142/s0219498821500791

Abstract (EN): We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of N-d with finite complement in N-d. These semigroups are affine semigroups, which in particular implies that they are finitely generated. For a given finite set of elements in N-d we show how to deduce if the monoid spanned by this set is a generalized numerical semigroup and, if so, we calculate its set of gaps. Also, given a finite set of elements in N-d we can determine if it is the set of gaps of a generalized numerical semigroup and, if so, compute the minimal generators of this monoid. We provide a new algorithm to compute the set of all generalized numerical semigroups with a prescribed genus (the cardinality of their sets of gaps). Its implementation allowed us to compute (for various dimensions) the number of numerical semigroups of higher genus than has previously been computed.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 24