论文标题
通过边缘标签的无垫图形布置和强烈弦图的表征
MAT-free graphic arrangements and a characterization of strongly chordal graphs by edge-labeling
论文作者
论文摘要
由于Abe-Barakat-Cuntz-Hoge-Hoge-Hoge-Terao（2016），多个添加定理（MAT）证明了Weyl排列的理想子军被证明是免费的。它们在迄今为止已知是自由的Weyl子部分中形成了重要的类。 Cuntz-M {ü} Cksch（2020）最近引入了无MAT安排的概念，以捕获垫子的核心，该核心从FreeNess的角度扩大了理想的子安排。本文的目的是在类型$ a $ a $ weyl subarrangements（或图形布置）的情况下进行精确表征垫子杂交。众所周知，理想和自由的图形布置分别对应于单位间隔和弦图。我们证明，仅当基础图是强烈的弦上时，图形布置是不含MAT的。特别是，它肯定地回答了一个cuntz-m {ü} cksch的问题，即在图形排列的情况下，在本地化下封闭了垫子。
Ideal subarrangements of a Weyl arrangement are proved to be free by the multiple addition theorem (MAT) due to Abe-Barakat-Cuntz-Hoge-Terao (2016). They form a significant class among Weyl subarrangements that are known to be free so far. The concept of MAT-free arrangements was introduced recently by Cuntz-M{ü}cksch (2020) to capture a core of the MAT, which enlarges the ideal subarrangements from the perspective of freeness. The aim of this paper is to give a precise characterization of the MAT-freeness in the case of type $A$ Weyl subarrangements (or graphic arrangements). It is known that the ideal and free graphic arrangements correspond to the unit interval and chordal graphs respectively. We prove that a graphic arrangement is MAT-free if and only if the underlying graph is strongly chordal. In particular, it affirmatively answers a question of Cuntz-M{ü}cksch that MAT-freeness is closed under taking localization in the case of graphic arrangements.
