首页|Erdos-Ko-Rado theorems for ovoidal circle geometries and polynomials over finite fields
Erdos-Ko-Rado theorems for ovoidal circle geometries and polynomials over finite fields
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NSTL
Elsevier
In this paper we investigate Erdos-Ko-Rado theorems in ovoidal circle geometries. We prove that in Mobius planes of even order greater than 2, and ovoidal Laguerre planes of odd order, the largest families of circles which pairwise intersect in at least one point, consist of all circles through a fixed point. In ovoidal Laguerre planes of even order, a similar result holds, but there is one other type of largest family of pairwise intersecting circles. As a corollary, we prove that the largest families of polynomials over F-q of degree at most k, with 2 <= k < q, which pairwise take the same value on at least one point, consist of all polynomials f of degree at most k such that f(x) = y for some fixed x and y in F-q. We also discuss this problem for ovoidal Minkowski planes, and we investigate the largest families of circles pairwise intersecting in two points in circle geometries. (c) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
