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Erdős-Ko-Rado theorem for irreducible imprimitive reflection groups. (English) Zbl 1250.05118
Summary: Let $\Omega$ be a finite set, and let $G$ be a permutation group on $\Omega$. A subset $H$ of $G$ is called intersecting if any $\sigma, \pi \in H$ have 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 $\{1, \dots, n\}$ provided $n$ is sufficiently large.

05E10Combinatorial aspects of representation theory
20C15Ordinary representations and characters of groups
05D05Extremal set theory
Full Text: DOI
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