Erdos-Ko-Rado theorems on the weak Bruhat lattice

被引:0
|
作者
Fishel, Susanna [1 ]
Hurlbert, Glenn [2 ]
Kamat, Vikram [3 ]
Meagher, Karen [4 ]
机构
[1] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ USA
[2] Virginia Commonwealth Univ, Richmond, VA USA
[3] Villanova Univ, Villanova, PA 19085 USA
[4] Univ Regina, Regina, SK, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Erdos-Ko-Rado theorem; Bruhat lattice; Intersecting permutations; INTERSECTION-THEOREMS; SYSTEMS;
D O I
10.1016/j.dam.2018.12.019
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let L= (X, <=) be a lattice. For P subset of X we say that P is t-intersecting if rank(x boolean AND y) >= t for all x, y is an element of P. The seminal theorem of Erdos, Ko and Rado describes the maximum intersecting P, in the lattice of subsets of a finite set with the additional condition that P is contained within a level of the lattice. The Erdos-Ko-Rado theorem has been extensively studied and generalized to other objects and lattices. In this paper, we focus on intersecting families of permutations as defined with respect to the weak Bruhat lattice. In this setting, we prove analogs of certain extremal results on intersecting set systems. In particular we give a characterization of the maximum intersecting families of permutations in the Bruhat lattice. We also characterize the maximum intersecting families of permutations within the rth level of the Bruhat lattice of permutations of size n, provided that n is large relative to r. (C) 2018 Published by Elsevier B.V.
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页码:65 / 75
页数:11
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