CROSSINGS AND NESTINGS OF TWO EDGES IN SET PARTITIONS

被引:7
|
作者
Poznanovic, Svetlana [1 ]
Yan, Catherine [1 ,2 ]
机构
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[2] Nankai Univ, LPMC TJKLC, Ctr Combinator, Tianjin 300071, Peoples R China
关键词
set partitions; crossings; nestings; MATCHINGS;
D O I
10.1137/070705222
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let pi and lambda be two set partitions with the same number of blocks. Assume pi is a partition of [n]. For any integer l, m >= 0, let T (pi, l) be the set of partitions of [n + l] whose restrictions to the last n elements are isomorphic to p, and T (pi, l, m) the subset of T (pi, l) consisting of those partitions with exactly m blocks. Similarly define T (lambda, l) and T (lambda, l, m). We prove that if the statistic cr (ne), the number of crossings (nestings) of two edges, coincides on the sets T(pi, l) and T (lambda, l) for l = 0, 1, then it coincides on T (pi, l, m) and T (lambda, l, m) for all l, m >= 0. These results extend the ones obtained by Klazar on the distribution of crossings and nestings for matchings.
引用
收藏
页码:787 / 804
页数:18
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