论文标题
通过排列语言的组合生成。 V.无环方向
Combinatorial generation via permutation languages. V. Acyclic orientations
论文作者
论文摘要
1993年，Savage，Squire和West描述了一种能力构造，该构造准确地恰好翻转一个弧形，以产生弦弦图的每一个环形方向。我们提供了两个结果的概括。首先，我们描述了满足简单订购条件的超图的无环方向的灰色代码，这概括了完美的消除图的概念。这将Savage-Squire-West结构统一使用，该结构最近通过算法生成弦图的消除树。其次，我们考虑弦图的无环方向的晶格的商，并为它们提供灰色代码，以解决Pilaud提出的问题。这也概括了最近的一种算法，用于在对称组上产生弱顺序的晶格一致性。我们的算法源自Hartung-Hoang-Mütze-Williams组合生成框架，它们产生了简单的算法，用于计算汉密尔顿路径和周期，包括大型多型多型，包括弦琴巢穴和商potients。特别是，我们得出了野蛮的西方建筑的有效实施。一路上，我们概述了有关图和超图的无环方向的多面体和秩序理论方面的旧结果。
In 1993, Savage, Squire, and West described an inductive construction for generating every acyclic orientation of a chordal graph exactly once, flipping one arc at a time. We provide two generalizations of this result. Firstly, we describe Gray codes for acyclic orientations of hypergraphs that satisfy a simple ordering condition, which generalizes the notion of perfect elimination order of graphs. This unifies the Savage-Squire-West construction with a recent algorithm for generating elimination trees of chordal graphs. Secondly, we consider quotients of lattices of acyclic orientations of chordal graphs, and we provide a Gray code for them, addressing a question raised by Pilaud. This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group. Our algorithms are derived from the Hartung-Hoang-Mütze-Williams combinatorial generation framework, and they yield simple algorithms for computing Hamilton paths and cycles on large classes of polytopes, including chordal nestohedra and quotientopes. In particular, we derive an efficient implementation of the Savage-Squire-West construction. Along the way, we give an overview of old and recent results about the polyhedral and order-theoretic aspects of acyclic orientations of graphs and hypergraphs.
