顶点加权有向图与Shi和Ish之间的排列的自由性
Vertex-weighted Digraphs and Freeness of Arrangements Between Shi and Ish
AI总结：
本文引入顶点加权有向图排列，统一了Shi与Ish之间的排列，证明其自由性，并指出仅Ish排列具有超可解锥。
摘要：
我们从组合学和自由性的角度引入并研究了Stanley的$\psi$-图排列的有向图类比。我们的排列构成了文献中各种排列类别的共同推广，包括Catalan排列、Shi排列、Ish排列，尤其是最近由Duarte和Guedes de Oliveira引入的介于Shi和Ish之间的排列。我们证明了介于Shi和Ish之间的所有排列都具有相同的特征多项式，且所有根均为整数，从而自然提出了它们的自由性问题。我们在有向图上定义了两种操作，称为king和coking消除操作，并证明在权重$\psi$满足一定条件下，这些操作保持相关排列的特征多项式和自由性。作为应用，我们肯定地证明了介于Shi和Ish之间的所有排列都是自由的，并且其中只有Ish排列具有超可解锥。
英文摘要：
We introduce and study a digraph analogue of Stanley's $ψ$-graphical arrangements from the perspectives of combinatorics and freeness. Our arrangements form a common generalization of various classes of arrangements in literature including the Catalan arrangement, the Shi arrangement, the Ish arrangement, and especially the arrangements interpolating between Shi and Ish recently introduced by Duarte and Guedes de Oliveira. The arrangements between Shi and Ish all are proved to have the same characteristic polynomial with all integer roots, thus raising the natural question of their freeness. We define two operations on digraphs, which we shall call king and coking elimination operations and prove that subject to certain conditions on the weight $ψ$, the operations preserve the characteristic polynomials and freeness of the associated arrangements. As an application, we affirmatively prove that the arrangements between Shi and Ish all are free, and among them only the Ish arrangement has supersolvable cone.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
