Young Diagram Decompositions for Almost Symmetric Numerical Semigroups

Abstract

This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams, which enables a visual and algorithmic approach to studying properties of numerical semigroups. Central to the paper, a decomposition theorem for almost symmetric numerical semigroups is proved, which reveals that such semigroups can be uniquely expressed as a combination of a numerical semigroup, its dual and an ordinary numerical semigroup.