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Articles 1 - 9 of 9
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
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
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 $X.$
On Isolated Gaps In Numerical Semigroups, Harold J. Smith
On Isolated Gaps In Numerical Semigroups, Harold J. Smith
Turkish Journal of Mathematics
A numerical semigroup is said to be perfect if it does not contain any isolated gaps. In this paper, we will look at some basic properties of isolated gaps in numerical semigroups. In particular, we will see how they are related to elements of the Apery set. We will use these properties to find all of the isolated gaps in a numerical semigroup of embedding dimension two and demonstrate a simple method of generating some examples of perfect numerical semigroups of embedding dimension three.
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel
Turkish Journal of Mathematics
IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Turkish Journal of Mathematics
In this paper, we introduce almost symmetric Arf partitions (for short, ASA-partitions) and using properties of partitions of positive integers, we give the number of almost symmetric Arf semigroups of genus $g$.
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
4-Generated Pseudo Symmetric Monomial Curves With Not Cohen-Macaulay Tangent Cones, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, standard bases of some toric ideals associated to 4-generated pseudo symmetric semigroups with not Cohen-Macaulay tangent cones at the origin are computed. As the tangent cones are not Cohen-Macaulay, nondecreasingness of the Hilbert function of the local ring was not guaranteed. Therefore, using these standard bases, Hilbert functions are explicitly computed as a step towards the characterization of Hilbert function. In addition, when the smallest integer satisfying $k(\alpha_2+1)
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
Turkish Journal of Mathematics
The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups. We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.
Perfect Numerical Semigroups, María Ángeles Moreno Frías, Jose Carlos Rosales
Perfect Numerical Semigroups, María Ángeles Moreno Frías, Jose Carlos Rosales
Turkish Journal of Mathematics
A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfect numerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them. We also study the perfect monoid, which is a subset of $\N$ that can be expressed as an intersection of perfect numerical semigroups, and we present the perfect monoid generated by a subset of $\N$. We give an algorithm to calculate it. We study the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embedding dimension, …
Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda
Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda
Turkish Journal of Mathematics
We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than or equal to $4g-1$.