Şahin, Nil2021-03-042021-03-0420201300-0098http://hdl.handle.net/11693/75763In 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(α2 + 1) < (k − 1)α1 + (k + 1)α21 + α3 is 1, it is proved that the Hilbert function of the local ring is nondecreasing.EnglishHilbert functionTangent coneMonomial curveNumerical semigroupStandard basesArticle10.3906/mat-1910-92