On the combinatories of balanced incomplete block designs

Date of Publication

1995

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This thesis presents the applications of Combinatorics in a Balanced Incomplete Block Design (B.I.B.D). A BIBD is a block design with parameters (v, b, r, k, ) consisting of v elements called varieties and subsets of these v elements called blocks and which satisfies four conditions: (1) no variety appears more than once in a block (2) every variety appears equally often, r times (3) every (unordered) pair of varieties appears in the same number of blocks, denoted by and (4) the block size, k, is constant. It is shown that the dual of BIBD is also a BIBD if and only if the design is symmetric, that is v = b.The researchers expounded on some of the sections of the first two chapters of the book entitled Combinatorics of Experimental Design by Anne Penfold Street and Deborah J. Street. All proofs of the theorems in this thesis are restatements of the proofs in the aforementioned book, but are more detailed in manner. Also, some exercises were solved and an illustration of the BIBD problem was presented.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU07034

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

88 leaves

Keywords

Combinatorial designs and configurations; Block designs; Experimental design

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