Contractions of a numerical semigroup

Addition Behavior of a Numerical Semigroup 23

— In this work we study some objects describing the addition behavior of a numerical semigroup and we prove that they uniquely determine the numerical semigroup. We then study the case of Arf numerical semigroups and find some specific results. Résumé (Comportement de l’addition dans un semi-groupe numérique). — Dans ce travail, nous étudions des objets qui décrivent le comportement de l’additi...

The Numerical Semigroup of Phrases' Lengths in a Simple Alphabet

Let A be an alphabet with two elements. Considering a particular class of words (the phrases) over such an alphabet, we connect with the theory of numerical semigroups. We study the properties of the family of numerical semigroups which arise from this starting point.

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Numerical Range and Quasi - Sectorial Contractions

We apply a method developed by one of the authors, see [1], to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups {exp(−tS)}t≥0, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation: e...

The Complexity of the Numerical Semigroup Gap Counting Problem

In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined as a positive integer that does not belong to the numerical semigroup. The computation of gaps of numerical semigroups has been actively studied from the 19t...