|
|||||
|
|
Weighted intriguing sets of finite generalised quadrangles |
|
| Authors: | John Bamberg Alice Devillers Jeroen Schillewaert |
| Institution: | 1. The Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, 6009, WA, Australia 2. Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand 3. Service de G??om??trie, Combinatoire et Th??orie des Groupes, D??partement de Math??matique, Universit?? Libre de Bruxelles, ULB, CP 216, Boulevard du Triomphe, 1050, Bruxelles, Belgique |
| Abstract: | We construct and analyse interesting integer valued functions on the points of a generalised quadrangle which lie in the orthogonal complement of a principal eigenspace of the collinearity relation. These functions generalise the intriguing sets introduced by Bamberg et al. (Combinatorica 29(1):1?C17, 2009), and they provide the extra machinery to give new proofs of old results and to establish new insight into the existence of certain configurations of generalised quadrangles. In particular, we give a geometric characterisation of Payne??s tight sets, we give a new proof of Thas?? result that an m-ovoid of a generalised quadrangle of order (s,s 2) is a hemisystem, and we give a bound on the values of m for which it is possible for an m-ovoid of the four dimensional Hermitian variety to exist. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |