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Full-Text Articles in Physical Sciences and Mathematics
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)