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9063 results in Discrete Mathematics, Information Theory and Coding

Page 1 of 454

The Shrikhande Graph
  • A Window on Discrete Mathematics
  • Peter J. Cameron, Aparna Lakshmanan S., Ambat Vijayakumar
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • The Shrikhande graph, discovered by Indian Mathematician Sharadchandra Shankar Shrikhande in 1959, exhibits several unusual properties and occupies a pivotal position within discrete mathematics. Offering a unique introduction to graph theory and discrete mathematics, this book uses the example of the Shrikhande graph as a window through which these topics can be explored. Providing historical background, including the Euler conjecture and its demise, the authors explore key concepts including: Cayley graphs; topological graph theory; spectral theory; Latin squares; root systems. A novel and valuable resource for graduate students and researchers interested in graph theory, its history, and applications, this book offers a comprehensive exploration of the Shrikhande graph and its significance.

Games on Graphs
  • From Logic and Automata to Algorithms
  • Edited by ‪Nathanaël Fijalkow
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    30 April 2026
  • This volume introduces the fundamental results and the state of the art in infinite duration games on graphs. These versatile game models first appeared in the study of automata and logic, but later became important for program verification and synthesis. They have many more applications. In particular, this book covers models from the fields of optimisation, reinforcement learning, model theory, and set theory. The material is presented at a level accessible to beginning graduate students, requiring only a basic understanding of discrete algorithms and graphs. The book's primary objective is constructing efficient algorithms for analysing different types of games. Rather than describe their implementation in full detail, it investigates their theoretical foundations and proves their properties and winning strategies. This tutorial reference from experts across the field is ideal for students, researchers, and professionals in logic and automata, verification and synthesis, and related fields.

Basic Graph Theory
  • Béla Bollobás, Robert Morris
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    30 April 2026
  • Over the past few decades, graph theory has developed into one of the central areas of modern mathematics, with close (and growing) connections to areas of pure mathematics such as number theory, probability theory, algebra and geometry, as well as to applied areas such as the theory of networks, machine learning, statistical physics, and biology. It is a young and vibrant area, with several major breakthroughs having occurred in just the past few years. This book offers the reader a gentle introduction to the fundamental concepts and techniques of graph theory, covering classical topics such as matchings, colourings and connectivity, alongside the modern and vibrant areas of extremal graph theory, Ramsey theory, and random graphs. The focus throughout is on beautiful questions, ideas and proofs, and on illustrating simple but powerful techniques, such as the probabilistic method, that should be part of every young mathematician's toolkit.

Extremal Graph and Hypergraph Theory
  • With Ramsey Theory
  • Dhruv Mubayi, Jacques A. Verstraete
  • Coming soon
  • Expected online publication date:
    March 2026
    Print publication:
    31 March 2026
  • Providing a cohesive reference for advanced undergraduates, graduate students and even experienced researchers, this text contains both introductory and advanced material in extremal graph theory, hypergraph theory and Ramsey theory. Along the way, the book includes many modern proof techniques in the field such as the probabilistic method and algebraic methods. Several recent breakthroughs are presented with complete proofs, for example, recent results on the sunflower problem, and off-diagonal and geometric Ramsey theory. It is perhaps unique in containing material on both hypergraph regularity and containers. Featuring an extensive list of exercises, the text is suitable as a teaching text for a variety of courses in extremal combinatorics. Each of the two parts can form the basis of separate courses, and the majority of sections are designed to match the length of a single lecture.

Coding for Erasure Channels
  • Enrico Paolini, Gianluigi Liva, Balázs Matuz, Marco Chiani
  • Coming soon
  • Expected online publication date:
    February 2026
    Print publication:
    28 February 2026
  • Understand how to make wireless communication networks, digital storage systems and computer networks robust and reliable in the first unified, comprehensive treatment of erasure correcting codes. Data loss is unavoidable in modern computer networks; as such, data recovery can be crucial and these codes can play a central role. Through a focused, detailed approach, you will gain a solid understanding of the theory and the practical knowledge to analyze, design and implement erasure codes for future computer networks and digital storage systems. Starting with essential concepts from algebra and classical coding theory, the book provides specific code descriptions and efficient design methods, with practical applications and advanced techniques stemming from cutting-edge research. This is an accessible and self-contained reference, invaluable to both theorists and practitioners in electrical engineering, computer science and mathematics.

Page 1 of 454