Designs And Graphs

In 1988, the news of Egmont Köhler's untimely death at the age of 55 reached his friends and colleagues. It was widely felt that a lasting memorial tribute should be organized. The result is the present volume, containing forty-two articles, mostly in combinatorial design theory and graph theory, and all in memory of Egmont Köhler. Designs and graphs were his areas of particular interest; he will long be remembered for his research on cyclic designs, Skolem sequences, t-designs and the Oberwolfach problem. Professors Lenz and Ringel give a detailed appreciation of Köhler's research in the first article of this volume. There is, however, one aspect of Egmont Köhler's biography that merits special attention. Before taking up the study of mathematics at the age of 31, he had completed training as a musician (studying both composition and violoncello at the Musikhochschule in Berlin), and worked as a cellist in a symphony orchestra for some years. This accounts for his interest in the combinatorial aspects of music. His work and lectures in this direction had begun to attract the interest of many musicians, and he had commenced work on a book on mathematical aspects of musical theory. It is tragic indeed that his early death prevented the completion of his work; the surviving paper on the classification and complexity of chords indicates the loss that his death meant to the area, as he was almost uniquely qualified to bring mathematics and music together, being a professional in both fields.

This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.

This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.

Graphical practice. Theory of data graphics.

Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Elements of Graph Design is for anyone who creates graphs, whether by computer or by pencil and paper. It is for anyone who relies on graphs in school work, presentations, or business reports. It is for anyone who wants a better understanding of the graphs used by newspapers and magazines, politicians, and advertisers (Kosslyn includes a chapter on how graphs can be used to misrepresent data). Finally it is for anyone interested in the mechanics of perception, memory, and cognition that come into play not just when we read graphs, but in any visual encounter