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)
Hilbert function, tangent cone, monomial curve, numerical semigroup, standard bases
"4-generated pseudo symmetric monomial curves with not Cohen-Macaulay tangent cones,"
Turkish Journal of Mathematics: Vol. 44:
6, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss6/16