Dyck paths and positroids from unit interval orders
Dyck paths and positroids from unit interval orders
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单位间隔阶数的 Dyck 路径和正类
DOI：
10.1016/j.jcta.2017.09.005
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
F. Gotti
中科院分区：
文献类型：
--
作者：
A. Chavez;F. Gotti
众所周知，[n]上的非同构单位区间阶的个数等于第n个Catalan数。利用Skandera和Reed的工作以及Postnikov的工作，我们证明了[n]上的每一个单位区间序都自然地诱导出[2 n]上的一个秩为n的正胚.我们把以这种方式产生的正粒称为单位区间正粒。我们通过描述它们的相关装饰排列来刻画单位区间正粒，证明每一个都必须是编码长度为2n的Dyck路径的2n-圈。我们还提供了食谱读取的装饰置换的单位区间正拟阵P从反邻接矩阵和区间表示的单位区间秩序诱导P.使用我们的表征的装饰置换，我们描述了Le图对应的单位区间正拟阵。此外，我们给出了两个由单位区间正粒参数化的Grassmann胞腔在Grassmann胞腔复形内相邻的充要条件。最后，我们提出了一个潜在的方法来找到一个单位区间顺序的f-向量。
It is well known that the number of non-isomorphic unit interval orders on [n] equals the n-th Catalan number. Using work of Skandera and Reed and work of Postnikov, we show that each unit interval order on [n] naturally induces a rank n positroid on [2 n]. We call the positroids produced in this fashion unit interval positroids. We characterize the unit interval positroids by describing their associated decorated permutations, showing that each one must be a 2n-cycle encoding a Dyck path of length 2n. We also provide recipes to read the decorated permutation of a unit interval positroid P from both the antiadjacency matrix and the interval representation of the unit interval order inducing P. Using our characterization of the decorated permutation, we describe the Le-diagrams corresponding to unit interval positroids. In addition, we give a necessary and sufficient condition for two Grassmann cells parameterized by unit interval positroids to be adjacent inside the Grassmann cell complex. Finally, we propose a potential approach to find the f-vector of a unit interval order.
影响因子：
1.3
作者：
Federico Ardila;F. Rincón;L. Williams
通讯作者：
Federico Ardila;F. Rincón;L. Williams