On reducible non-Weierstrass semigroups
J. I. Garc\'ia-Garc\'ia, D. Mar\'in-Arag\'on, F. Torres, A., Vigneron-Tenorio
TL;DR
This paper introduces a new family of non-Weierstrass semigroups formed by intersections of Weierstrass semigroups and provides methods to compute non-Weierstrass semigroups with arbitrarily large genus.
Contribution
It presents a novel construction of non-Weierstrass semigroups as intersections of known semigroups and offers algorithms for their calculation at large genus.
Findings
New family of non-Weierstrass semigroups identified
Methods for calculating large genus non-Weierstrass semigroups developed
Intersection approach links Weierstrass and non-Weierstrass semigroups
Abstract
Weierstrass semigroups are well-known along the literature. We present a new family of non-Weierstrass semigroups which can be written as an intersection of Weierstrass semigroups. In addition, we provide methods for calculating non-Weierstrass semigroups with genus as large as desired.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Advanced Algebra and Logic