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TÜBİTAK

Turkish Journal of Mathematics

Journal

2023

Numerical semigroup

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n Jan 2023

On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n

Turkish Journal of Mathematics

In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.


The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales Jan 2023

The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales

Turkish Journal of Mathematics

A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$