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The study of combinatorial block designs is a vibrant area of combinatorial mathematics with connections to finite geometries, graph theory, coding theory and statistics. The practice of ordering combinatorial objects can trace its roots to bell ringing which originated in 17th century England, but only emerged as a significant modern research area with the work of F. Gray and N. de Bruijn.  These two fascinating areas of mathematics are brought together for the first time in this book. It presents new terminology and concepts which unify existing and recent results from a wide variety of sources. In order to provide a complete introduction and survey, the book begins with background material on combinatorial block designs and combinatorial orderings, including Gray codes — the most common and well-studied combinatorial ordering concept — and universal cycles. The central chapter discusses how ordering concepts can be applied to block designs, with definitions from existing (configuration orderings) and new (Gray codes and universal cycles for designs) research. Two chapters are devoted to a survey of results in the field, including illustrative proofs and examples. The book concludes with a discussion of connections to a broad range of applications in computer science, engineering and statistics. This book will appeal to both graduate students and researchers. Each chapter contains worked examples and proofs, complete reference lists, exercises and a list of conjectures and open problems. Practitioners will also find the book appealing for its accessible, self-contained introduction to the mathematics behind the applications.

Block designs. --- Gray codes. --- Mathematics. --- Block designs --- Gray codes --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Statistics --- Designs, Block --- Reflected binary codes --- Reflective binary codes --- Computer science --- Combinatorics. --- Mathematics, general. --- Discrete Mathematics in Computer Science. --- Binary system (Mathematics) --- Coding theory --- Combinatorial analysis --- Combinatorial designs and configurations --- Experimental design --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Math --- Science --- Combinatorics --- Mathematical analysis --- Computer science—Mathematics.

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This book constitutes the refereed proceedings of the 19th International Workshop on Modelling and Mining Networks, WAW 2024, held in Warsaw, Poland, during June 3–6, 2024. The 12 full papers presented in this book were carefully reviewed and selected from 19 submissions. The aim of this workshop was to further the understanding of networks that arise in theoretical as well as applied domains. The goal was also to stimulate the development of high-performance and scalable algorithms that exploit these networks. .

Computer science. --- Data structures (Computer science). --- Information theory. --- Application software. --- Computer science --- Discrete mathematics. --- Theory of Computation. --- Data Structures and Information Theory. --- Computer and Information Systems Applications. --- Discrete Mathematics in Computer Science. --- Mathematics. --- Data structures (Computer science)