标题： 几乎对称数值半群的杨图分解 显示英文标题

标题： Young Diagram Decompositions for Almost Symmetric Numerical Semigroups

摘要： 本文通过杨图的组合视角引入了几乎对称数值半群的新结构分解。为此，我们使用了数值集与杨图之间的基础对应关系，这使得可以通过视觉和算法的方法来研究数值半群的性质。文章的核心在于证明了一个关于几乎对称数值半群的分解定理，该定理揭示了此类半群可以唯一地表示为一个数值半群、其对偶以及一个普通数值半群的组合。 显示英文摘要

摘要： 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.