Some properties of crossings and partitions

被引：101
|
作者：
Biane, P [1 ]
机构：
[1] UNIV PARIS 06,CNRS,PROBABIL LAB,F-75251 PARIS 05,FRANCE
来源：
DISCRETE MATHEMATICS | 1997年 / 175卷 / 1-3期
关键词：
D O I：
10.1016/S0012-365X(96)00139-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a group theoretical interpretation of the lattice of non-crossing partitions of a cycle of length m. Using this interpretation, we prove that the group of skew-automorphisms of this lattice is isomorphic to the dihedral group D-4m. We also give some generating functions, in terms of continued fraction expansions, for some statistics on the set of partitions involving the number of restricted crossings and the number of classes.
引用
收藏
页码：41 / 53
页数：13
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