The aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. The last five chapters of the book are devoted to balanced generalized weighing matrices, decomposable symmetric designs, subdesigns of symmetric designs, non-embeddable quasi-residual designs, and Ryser designs. Most results in these chapters have never previously appeared in book form. The book concludes with a comprehensive bibliography of over 400 entries.Researchers in all areas of combinatorial designs, including coding theory and finite geometries, will find much of interest here. Detailed proofs and a large number of exercises make this book suitable as a text for an advanced course in combinatorial designs.
Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this book the authors discuss the generalization of results and applications to quasi-symmetric designs. The coverage is comprehensive and will be useful for researchers and graduate students. An attractive feature is the discussion of unsolved problems.
A *-design is a family of v subsets (blocks) of a v-set such that any two distinct blocks intersect in * points and not all blocks have the same cardinality. Ryser's and Woodall's *-design conjecture states that each *-design can be obtained from a symmetric design by complementing with respect to a fixed block. We prove this conjecture for v=p+1, 2p+1, 3p+1, where p is prime.
In this paper we use incidence matrices of block designs and row±column designs to obtain combinatorial inequalities. We introduce the concept of nearly orthogonal Latin squares by modifying the usual de®nition of orthogonal Latin squares. This concept opens up interesting combinatorial problems and is expected to be useful in planning experiments by statisticians.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.