Şahin, Nil2025-02-172025-02-172024-07-140092-7872https://hdl.handle.net/11693/116288In this article we solve the following problem: “The Hilbert function of thelocal ring of a 4-generated pseudo-symmetric numerical semigroup is alwaysnon-decreasing.” We give a complete characterization of the standard baseswhen the tangent cone is not Cohen-Macaulay by showing that the number ofelements in the standard basis depends on some parameters we define. Sincethe tangent cone is not Cohen-Macaulay, non-decreasingness of the Hilbertfunction was not guaranteed, thus we proved the non-decreasingness fromour explicit Hilbert function computation.EnglishCC BY 4.0 (Attribution 4.0 International Deed)https://creativecommons.org/licenses/by/4.0/Hilbert functionMonomial curveNumerical semigroupStandard basesTangent coneArticle10.1080/00927872.2024.23607101532-4125