Positroids and non-crossing partitions
Positroids and non-crossing partitions
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DOI：
10.1090/tran/6331
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发表时间：
2013-08
影响因子：
1.3
通讯作者：
Federico Ardila;F. Rincón;L. Williams
中科院分区：
文献类型：
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作者：
Federico Ardila;F. Rincón;L. Williams
我们调查的作用，非交叉分区的研究中发挥的positroids，一类拟阵介绍Postnikov。我们证明了每一个正拟阵都可以通过在基集上选择一个不相交的划分，然后自由地将一个连通正拟阵的结构放置在该划分的每个块上来唯一地构造。这个结构结果产生了关于正粒子的几个组合事实。我们证明了正拟多面体的面偏序集嵌入在加权非交叉划分的偏序集中。我们列举了连接的正粒子，并显示它们是如何自然产生的自由概率。最后，我们证明了[n]上正拟阵连通的概率渐近等于1/e^2。
We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground set, and then freely placing the structure of a connected positroid on each of the blocks of the partition. This structural result yields several combinatorial facts about positroids. We show that the face poset of a positroid polytope embeds in a poset of weighted non-crossing partitions. We enumerate connected positroids, and show how they arise naturally in free probability. Finally, we prove that the probability that a positroid on [n] is connected equals 1/e^2 asymptotically.