Erdős-Ko-Rado theorem for irreducible imprimitive reflection groups

Abstract

Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any σ, π ∈ H, they agree on at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group G(m, p, n) is a coset of the stabilizer of a point in {1, …, n} provided n is sufficiently large.

Keywords

Erdős-Ko-Rado theorem / representation theory / imprimitive reflection groups

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