论文标题
在与有导图有关的Manin-Schechtman订单上
On Manin-Schechtman orders related to directed graphs
论文作者
论文摘要
作为对排列弱的订单的概括，1989年，Manin和Schechtman在集合$ [n] = \ {1,2，\ ldots，n \} $的$ D $ - 元素子集上引入了更高的bruhat订单概念。在该领域的其他结果中，他们证明了$ n，d $固定的此类订单集，并具有自然的局部转换，构成了一个poset，其中一个最小和一个最大元素。在本文中，我们考虑了一个更广泛的模型，该模型涉及一定符号的一定符合图的某些路径系统上所谓的凸顺序，在此类订单上引入局部变换或翻转，并证明所得结构给出了一个最小和一个最大元素的poset，从而产生了上述典型的典型元素。
As a generalization of weak Bruhat orders on permutations, in 1989 Manin and Schechtman introduced the notion of a higher Bruhat order on the $d$-element subsets of a set $[n]=\{1,2,\ldots,n\}$. Among other results in this field, they proved that the set of such orders for $n,d$ fixed, endowed with natural local transformations, constitutes a poset with one minimal and one maximal elements. In this paper we consider a wider model, involving the so-called convex order on certain path systems in an acyclic directed graph, introduce local transformations, or flips, on such orders and prove that the resulting structure gives a poset with one minimal and one maximal elements as well, yielding a generalization of the above-mentioned classical result.
