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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.

MSC:

05E10 Combinatorial aspects of representation theory
20C15 Ordinary representations and characters
05D05 Extremal set theory
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