The Erdős-Ko-Rado theorem for the derangement graph of the projective general linear group acting on the projective space. (English) Zbl 1416.05276
Summary: In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group \({\mathrm{PGL}}_{n + 1}(q)\), in its natural action on the points of the \(n\)-dimensional projective space, is either a coset of the stabiliser of a point or a coset of the stabiliser of a hyperplane. This gives a positive solution to [K. Meagher and P. Spiga, J. Comb. Theory, Ser. A 118, No. 2, 532–544 (2011; Zbl 1227.05163), Conjecture 2].
MSC:
| 05D05 | Extremal set theory |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
Citations:
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