Perfect Mendelsohn designs with block size six

被引：20

作者：

Abel, RJR

Bennett, FE

Zhang, H

机构：

[1] Univ New S Wales, Sch Math, Kensington, NSW 2033, Australia

[2] Mt St Vincent Univ, Dept Math, Halifax, NS B3M 2J6, Canada

[3] Univ Iowa, Dept Comp Sci, Iowa City, IA 52240 USA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2000年 / 86卷 / 02期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

perfect Mendelsohn designs; Holey perfect Mendelsohn designs; balanced incomplete block designs; group divisible designs;

D O I：

10.1016/S0378-3758(99)00114-7

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A necessary condition for the existence of a (v, k, lambda,)-perfect Mendelsohn design is lambda v(v-1) = 0 (mod k). For k = 6 and lambda = 1, this condition gives v = 0, 1,3 or 4 (mod 6). Miao and Zhu have investigated the cases v = 0,1 (mod 6). This paper provides several improvements on their results and also investigates the cases v = 3,4 (mod 6). For v = 1 (mod 6) we solve the problem completely; for v = 0, 3, 4 (mod 6), the largest unknown cases are for v = 198, 657, 148, respectively. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：287 / 319

页数：33

共 31 条

[1]

Abel RJR., 1996, C.R.C. Handbook of Combinatorial Designs, P111

[2]

[Anonymous], 1985, DESIGN THEORY

[3] Perfect Mendelsohn Packing Designs with Block Size Five [J].