TY - JOUR

T1 - Erdős–Ko–Rado theorems on the weak Bruhat lattice

AU - Fishel, Susanna

AU - Hurlbert, G.

AU - Kamat, Vikram

AU - Meagher, K.

N1 - Funding Information:
Karen Meagher’s research is supported in part by NSERC Discovery Research Grant Application number RGPIN-341214-2013 . Susanna Fishel’s is partially supported by a collaboration grant for mathematicians from the Simons Foundation , grant number 359602 . Glenn Hurlbert’s research is supported in part by the Simons Foundation , grant number 246436 . Glenn Hurlbert and Vikram Kamat wish to acknowledge the support of travel grant number MATRP14-17 from the Research Fund Committee of the University of Malta . This grant enabled them to travel to the 2MCGTC2017 conference in Malta where some of this research was completed. The authors also wish to thank the referees for useful comments that helped improve this article.
Publisher Copyright:
© 2018

PY - 2019/8/15

Y1 - 2019/8/15

N2 - Let ℒ=(X,⪯) be a lattice. For P⊆X we say that P is t-intersecting if rank(x∧y)≥t for all x,y∈P. The seminal theorem of Erdős, 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 Erdős–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.

AB - Let ℒ=(X,⪯) be a lattice. For P⊆X we say that P is t-intersecting if rank(x∧y)≥t for all x,y∈P. The seminal theorem of Erdős, 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 Erdős–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.

KW - Bruhat lattice

KW - Erdős–Ko–Rado theorem

KW - Intersecting permutations

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U2 - 10.1016/j.dam.2018.12.019

DO - 10.1016/j.dam.2018.12.019

M3 - Article

AN - SCOPUS:85059849926

VL - 266

SP - 65

EP - 75

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -