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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Qing Xiang, University of Delaware, USA

Inviter: 陈绍示
Title:
Characterization of Intersecting Families of Maximum Size in PSL(2, q)
Time & Venue:
2018.4.19 15:00-16:00 N205
Abstract:
The Erdos-Ko-Rado (EKR) theorem is a classical result in extremal set
theory. It states that when k < n/2, any family of k-subsets of an n-set X,
with the property that any two subsets in the family have nonempty
intersection, has size at most binomial(n-1, k-1); equality holds if and only if the family
consists of all k-subsets of X containing a fixed point.

Here we consider EKR type problems for permutation groups. In particular, we focus on 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 in S, there exists an element x in PG(1, q)
such that g1(x) = g2(x). It is known that the maximum size of an intersecting
family in PSL(2, q) is q(q-1) = 2. We prove that all intersecting families of
maximum size are cosets of point stabilizers for all odd prime powers q > 3.
This is a joint work with Ling Long, Rafael Plaza, and Peter Sin.

 

 

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