Characterizing geometric designs, II

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Jungnickel, Dieter

关键词: 2-Design;    Geometric design;    Quasi-symmetric design;    Characterization theorems;   

DOI  :  10.1016/j.jcta.2010.05.004

来源: Elsevier

【 摘 要 】

We provide a characterization of the classical point-line designs PG(1) (n, q), where n >= 3, among all non-symmetric 2-(v, k, 1)-designs as those with the maximal number of hyperplanes. As an application of this result, we characterize the classical quasi-symmetric designs PG(n-2)(n, q), where n >= 4, among all (not necessarily quasi-symmetric) designs with the same parameters as those having line size q + 1 and all intersection numbers at least q(n-4) + ... + q + 1. Finally, we also give an explicit lower bound for the number of non-isomorphic designs having the same parameters as PG(1) (n, q); in particular, we obtain a new proof for the known fact that this number grows exponentially for any fixed value of q. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free