THE THEORETICAL INVESTIGATION OF THE BLOCK DESIGNS.
Abstract
The report is divided into seven sections. A brief exposition of the incidence matrix of the balanced incomplete block (BIB) design is given in section 1. The Hasse-Minkowski p-invariant of the rational congruence is discussed in section 2. In section 3, the necessary condition for existence of a symmetrical BIB design is given in terms of the Hasse-Minkowski p-invariant as the prototype of the non-existence proofs. In section 4, the properties of the association algebra of an association are presented with some examples of association schemes. Section 5 is devoted to the derivation of the necessary condition for existence of a regular and symmetrical partially balanced incomplete block (PBIB) design. The argument presented in section 5 is immediately carried over in section 6 to the derivation of the necessary condition for existence of a certain class of asymmetric PBIB designs. In section 7, the relationship algebra of a PBIB design is explained and some discussions of the non-existence proofs in connection with the relationship algebra are presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1968
- Accession Number
- AD0678209
Entities
People
- Junjiro Ogawa
Organizations
- Nihon University