“Block Design”的概念、定义、习题解题方法及翻译-数学辞典

单词

Block Design

释义

Block Design

An incidence system (, , , , ) in which a set of points is partitioned into a family of subsets (blocks) in such a way that any two points determine blocks with points in each block, andeach point is contained in different blocks. It is also generally required that , which is where the``incomplete'' comes from in the formal term most often encountered for block designs, Balanced Incomplete BlockDesigns (BIBD). The five parameters are not independent, but satisfy the two relations

(1)

(2)

A BIBD is therefore commonly written as simply (

), since

and

are given in terms of

, and

			(3)
			(4)

A BIBD is called Symmetric if

(or, equivalently,

Writing and , then the Incidence Matrix of the BIBD is given by the Matrix defined by

(5)

This matrix satisfies the equation

(6)

where

is a

Identity Matrix and

is a

matrix of 1s (Dinitz and Stinson 1992).

Examples of BIBDs are given in the following table.

Block Design	(, , )
Affine Plane	(, , 1)
Fano Plane	(7, 3, 1))
Hadamard Design	Symmetric (, , )
Projective Plane	Symmetric (, , 1)
Steiner Triple System	(, 3, 1)
Unital	(, , 1)

See also Affine Plane, Design, Fano Plane, Hadamard Design, Parallel Class, ProjectivePlane, Resolution, Resolvable, Steiner Triple System, Symmetric Block Design, Unital

References

Dinitz, J. H. and Stinson, D. R. ``A Brief Introduction to Design Theory.'' Ch. 1 in Contemporary Design Theory: A Collection of Surveys (Ed. J. H. Dinitz and D. R. Stinson). New York: Wiley, pp. 1-12, 1992.

Ryser, H. J. ``The -Configuration.'' §8.1 in Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., pp. 96-102, 1963.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。