Characterization of intersecting families of maximum size in PSL(2, q)

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Long, Ling¹  Plaza, Rafael²  Sin, Peter³  Xiang, Qing² 

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[3] Univ Florida, Dept Math, Gainesville, FL 32611 USA

关键词: Character table;    Erdos-Ko-Rado theorem;    Hypergeometric function over finite field;    Intersecting family;    Legendre sum;    Soto-Andrade sum;   

DOI  :  10.1016/j.jcta.2018.03.006

来源: Elsevier

【 摘 要 】

We consider the action of the 2-dimensional projective special linear group PSL(2, q) on the projective line PG(1, q) over the finite field F-q where q is an odd prime power. A subset S of PSL(2, q) is said to be an intersecting family if for any g1, g2 is an element of S, there exists an element x is an element of PG(1, q) such that x(91) = x(92). It is known that the maximum size of an intersecting family in PSL(2, q) is g(g 1)/2. We prove that all intersecting families of maximum size are cosets of point stabilizers for all odd prime powers q > 3. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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