On the combinatories of balanced incomplete block designs

• Main Authors: Altabano, Aimee U., Zarsadias, Lulitte C.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Combinatorial designs and configurations; Block designs; Experimental design
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16234
• Institution: De La Salle University

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.