广义四边形的一个组合性质

A Combinatorial Property of Generalized Quadrangle

在本文中我们主要得到结果是:令s是参数为s和t的广义四边形,设s≥t、若S有一个反正规点对(p,q),则对三元组(p,q,r),没有中心元的r的取法有(1/2)(t^3-t)十s^2-s+t-st^2种;有一个中心元的的r的取法有(t^2-1)(s-t)种;有两个中心元的r的取法有(1/2)(t^3-t)种。

In this paper we obtain mainly a result as follow: Let S be a generalized quadran- gle with parameters s and t. s≥t. If S has an antiregularpair (p. q). then there are 1/2 (t-t)+s^2t-st+t-st^2 points r smch that each triad (p, q. r) has zero centre, and there are (t^2-1) (s-t) points r that each triad (p. q. r) has one centre and there are 1/2 (t^3- t) points r that each triad (p, q, r) has two centres.