Erdős-Ko-Rado results for the general linear group, the special linear group and the affine general linear group

2021/10/18 by Meagher, Karen, Razafimahatratra, A. Sarobidy
#20B05 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05C35 #Secondary 05C69

paper · doi:10.48550/arxiv.2110.08972

Abstract

In this paper, we show that both the general linear group \glq and the special linear group \slgq have both the EKR property and the EKR-module property. This is done using an algebraic method; a weighted adjacency matrix for the derangement graph for the group is found and Hoffman's ratio bound is applied to this matrix. We also consider the group \aglq and the 2-intersecting sets in \PGL(2,q).

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