MAXIMAL AND MINIMAL COVERINGS OF (K-I)-TUPLES BY K-TUPLES

被引:19
作者
KALBFLEISCH, JG
STANTON, RG
机构
[1] University Of Waterloo, York University
关键词
D O I
10.2140/pjm.1968.26.131
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For m ≧ k, an (m, k) system is a set of A>tuples (A -subsets) of 1,2, … m. A minimal (m, k) system is an (m, k) system with the property that every (k − l)-tuple of the m elements appears in at least one k-tuple of the system, but no system with fewer k-tuples has this property. The numbers of fe-tuples in a minimal (m, k) system will be denoted by Nk(m). A maximal (m, k) is an (m, k) system with the property that no (k − l)-tuple appears in more than one k-tuple of the system, but no system with more A -tuples has this property. The number of A -tuples in a maximal (m, k) system is Dk(m). In this paper we shall be concerned with evaluating Nk and Dk and investigating the properties of extremal (m, k) systems for k − 2, 3. © 1968 by Pacific Journal of Mathematics.
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页码:131 / +
页数:1
相关论文
共 5 条
[1]   On the construction of balanced incomplete block designs [J].
Bose, RC .
ANNALS OF EUGENICS, 1939, 9 :353-399
[2]  
Fort Jr M., 1958, PAC J MATH, V8, P709
[3]  
Hanani H., 1960, CAN J MATH, V12, P145
[4]  
REISS M, 1959, CRELLE J, V56, P326
[5]  
STANTON RG, 1968, AEQUATIONES MATH, V1, P103