Erdős–Ko–Rado theorems on the weak Bruhat lattice

Susanna Fishel, G. Hurlbert, Vikram Kamat, K. Meagher

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)65-75
Number of pages11
JournalDiscrete Applied Mathematics
StatePublished - Aug 15 2019


  • Bruhat lattice
  • Erdős–Ko–Rado theorem
  • Intersecting permutations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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