用超椭圆构造强正则图(英文)  

Constructing new strongly regular graphs with hyperovals

作　　者：曹喜望[1] 胡沐辉[2] 

机构地区：[1]北京大学数学科学学院,北京100871 [2]黄冈师范学院数学系,湖北黄州438000

出　　处：《黄冈师范学院学报》2003年第3期12-14,共3页Journal of Huanggang Normal University

基　　金：黄冈师范学院科研基金项目 ( 98CA17)资助

摘　　要：在本文中 ,我们证明了下面主要结果 :如果 U=( X ,B)是一个 t-( v+t,k+t,1 )设计 ( t≥ 1 ) ,Y=( v1 ,v2 ,… ,vt)∈ X,用 UY表示 U在 Y上的限制 ,如果 D=UY是一个 2 -对称设计 ,并且 D中的超椭圆的个数至多为 tv( v-1 ) ( v-k) / [k( k2 -1 ) ],则这些超椭圆可以分为 t类 ,每一类构成一个 2 -设计 ,它们的块图都是强正则图 ,并且它们的并也是一个 2 -设计 .作为一个推论 ,我们给出了一个 2 -设计可以扩张的判据 。In this paper, we have proved the following main resul ts . If U Y=(X, B) is a (t+2)-(v+t, k+t, 1) design (t≥1), Y={v 1, v 2, ...v t}X. By U Y we denote the restriction of U on Y. If D=U Y is a square 2-(v, k, 1) design and the number of hyperovals in D is at most tv(v-1)(v-k)/k(k 2-1),then these hyperovals can be divided in to t classes, each of them contributes a 2-design and block graphs of them are strongly regular. Furthermore, the union of these designs is also a 2-desig n. As a corollary, we give a criterion of which design is extendable. Finally, w e give an example illustrating that our method works effectively.

关 键 词：区组设计 超椭圆 强正则图 组合数学 

分 类 号：O157.2[理学—数学]