Intriguing Sets in Partial Quadrangles

被引：8

作者：

Bamberg, John ^{[1
]}

De Clerck, Frank ^{[2
]}

Durante, Nicola ^{[3
]}

机构：

[1] Univ Western Australia, Sch Math & Stat, Crawley, WA 6009, Australia

[2] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

[3] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80125 Naples, Italy

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2011年 / 19卷 / 03期

关键词：

partial quadrangle; strongly regular graph; association scheme; TIGHT SETS; M-OVOIDS; HEMISYSTEMS;

D O I：

10.1002/jcd.20269

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The point-line geometry known as a partial quadrangle (introduced by Cameron in 1975) has the property that for every point/line non-incident pair (P, l), there is at most one line through P concurrent with l. So in particular, the well-studied objects known as generalized quadrangles are each partial quadrangles. An intriguing set of a generalized quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalized quadrangles by Bamberg, Law and Penttila to partial quadrangles, which gives insight into the structure of hemisystems and other intriguing sets of generalized quadrangles. (C) 2010 Wiley Periodicals, Inc. J Combin Designs 19: 217-245, 2011

引用

页码：217 / 245

页数：29