Imprimitive flag-transitive symmetric designs

被引：50
作者：
Praeger, Cheryl E. [1 ]
Zhou, Shenglin
机构：
[1] Univ Western Australia, Sch Math & Stat, Nedlands, WA 6009, Australia
[2] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES A | 2006年 / 113卷 / 07期
基金：
澳大利亚研究理事会;
关键词：
permutation group; flag-transitive; symmetric design;
D O I：
10.1016/j.jcta.2005.12.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A recent paper of O'Reilly Regueiro obtained an explicit upper bound on the number of points of a flag-transitive, point-imprimitive, symmetric design in terms of the number of blocks containing two points. We improve that upper bound and give a complete list of feasible parameter sequences for such designs for which two points lie in at most ten blocks. Classifications are available for some of these parameter sequences. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：1381 / 1395
页数：15
相关论文
共 24 条
[1]  
Beth T., 1986, DESIGN THEORY
[2]  
BOSE RC, 1939, ANN EUGEN, V9, P358
[3]   A root graph that is locally the line graph of the Petersen graph [J].
Brouwer, AE ;
Koolen, JH ;
Klin, MH .
DISCRETE MATHEMATICS, 2003, 264 (1-3) :13-24
[4]  
Camina A.R., 1994, J. Comb. Des., V2, P79
[5]   FLAG-TRANSITIVITY AND PRIMITIVITY [J].
DAVIES, H .
DISCRETE MATHEMATICS, 1987, 63 (01) :91-93
[6]   MOST BLOCK-TRANSITIVE T-DESIGNS ARE POINT-PRIMITIVE [J].
DELANDTSHEER, A ;
DOYEN, J .
GEOMETRIAE DEDICATA, 1989, 29 (03) :307-310
[7]  
Dinitz, 1996, CRC HDB COMBINATORIA
[8]  
Dixon JD., 1996, PERMUTATION GROUPS
[9]  
Fisher R. A., 1938, Statistical Tables for Biological, Agricultural
[10]  
Hughes D. R., 1985, Design theory
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