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Nil Şahin

Publications and source records attributed to Nil Şahin.

6 recordsLinked to original sources
arXiv2026

Numerical Semigroups of Sally Type II

In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $ν\ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We also construct a minimal resolution for another special class of such semigroups of type $ν-1$. Finally, we propose some conjectures for the Betti numbers of families of non-symmetric Sally type semigroups in the above cases in relation to those of the corresponding Gorenstein cases of Sally type semigroups.

math.AC↗
arXiv2024

On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves

In this article we solve the conjecture "Hilbert function of the local ring for a 4 generated pseudo-symmetric numerical semigroup $\langle n_1,n_2,n_3,n_4 \rangle$ is always non-decreasing when $ n_1 < n_2 < n_3 < n_4$". We give a complete characterization to the standard bases when the tangent cone is not Cohen-Macaulay by showing that the number of elements in the standard basis depends on some parameters $s_j$ 's we define. Since the tangent cone is not Cohen-Macaulay, non-decreasingness of the Hilbert fuction was not guaranteed, we proved the non-decreasingness from our explicit Hilbert Function computation.

math.AC↗
arXiv2019

4-Generated Pseudo Symmetric Monomial Curves with not Cohen-Macaulay Tangent Cones

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, non-decreasingness 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 $k(α_2+1)<(k-1)α_1+(k+1)α_{21}+α_3$ is $1$, it is proved that the Hilbert function of the local ring is non-decreasing.

math.AC↗
arXiv2018

Betti numbers for certain Cohen-Macaulay tangent cones

In this article, we compute Betti numbers for a Cohen-Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

math.AC↗
arXiv2018

On Pseudo Symmetric Monomial Curves

In this article, we study monomial curves, toric ideals and monomial algebras associated to $4$-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric ideals, give a characterization for these monomial algebras to have strongly indispensable minimal graded free resolutions. We also characterize when the tangent cones of these monomial curves at the origin are Cohen-Macaulay.

math.AC↗