Relationship of balanced incomplete block designs with finite geometries

vRELATIONSHIP OF BALANCED INCOMPLETE BLOCK DESIGNS WITHFINITE GEOMETRIES(M.Sc. Thesis)Nermin AVŞARGAZI UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYSeptember 2006ABSTRACTCombinatorial design theory concerns questions about whether it is possible toarrange elements of a finite set into subsets so that certain ?balanced?properties are satisfied. Types of designs that we will discuss include balancedincomplete block designs, t-designs, pairwise balanced designs and many more.Many of fundamental questions are existence questions: Does a design of aspecified type exist? Modern design theory includes many existence results aswell as nonexistence results. However, there remain many open problemsconcerning the existence of certain types of designs. Many types of designs thatare studied today were first considered in the context of mathematical puzzlesor brain-teasers in the 18th and 19th centuries. The study of design theory as amathematical discipline really began in the 20th century due to applications inthe design and analysis of statistical experiments. Designs have many otherapplications as well, such as tournament scheduling, lotteries, mathematicalbiology, algorithm design and analysis, networking, group testing andcryptography.Science Code : 205.1.066Key Words : t-Designs, BIBDs, pairwise balanced designsPage Number : 168Adviser : Prof.Dr. Hülya Bayrak