发表机构
School of Mathematics, Statistics, and Actuarial Science; University of Essex（数学、统计与精算科学学院; 埃塞克斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文给出有限半群组合D类存在置换匹配的充要条件，即结构矩阵存在平衡加权，并应用此条件证明n元链上保序自映射幺半群具有置换匹配。
AI 中文摘要
我们给出了有限半群的组合D类具有置换匹配的一个充要条件：其结构矩阵允许一个平衡加权，即具有恒定行和与恒定列和的非负权重。这削弱了正则性假设，Hall引理的角色由Birkhoff–von Neumann定理承担。然后我们应用此条件证明，n元链上所有保序自映射构成的幺半群具有置换匹配。
英文摘要
We give a necessary and sufficient condition for a combinatorial D-class of a finite semigroup to have a permutation matching: that its structure matrix admit a balanced weighting, that is, non-negative weights with constant row sums and constant column sums. This weakens the regularity hypothesis, the role of Hall's lemma being taken up by the Birkhoff--von Neumann theorem. We then apply it to show that the monoid of all order-preserving self-maps of an n-element chain, has a permutation matching.
Comments9 pages
