Journal of the
Korean Mathematical Society JKMS

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into a numerical semigroup and its dual. It is also given exactly for what kind of numerical semigroup $S$, the semigroup ring ${\mathbb k}[\![S]\!]$ has at least one Gorenstein subring and has at least one Kunz subring.

Keywords: Symmetric numerical semigroups, pseudo-symmetric numerical semigroups, Young diagrams, semigroup rings

MSC numbers: 20M14, 20M20, 20M25