Algebraic, Extremal and Metric Combinatorics 1986: A Research Compendium by M. Deza – Association Schemes, Extremal Prob

Introduction

For students and researchers delving into the deeper realms of combinatorial mathematics, Algebraic, Extremal and Metric Combinatorics 1986 stands as a landmark reference. Edited by the renowned M. Deza and published by Cambridge University Press, this hardcover volume captures the vibrant research presented at a seminal conference held at the University of Montreal. It offers a rigorous yet accessible gateway to three interconnected branches of combinatorics, making it an indispensable addition to any serious mathematics library in India.

Book Overview

This collection brings together selected, peer-reviewed papers that reflect the state of progress in algebraic, extremal, and metric combinatorics during the mid-1980s. The book is structured to guide readers from foundational concepts to advanced research frontiers. Each chapter presents new results, extensive surveys, and open problems, ensuring that the content remains relevant for both learning and reference. The inclusion of Ivanov's comprehensive survey on Soviet research provides a unique window into parallel developments that were often inaccessible to Western scholars at the time.

Key Highlights

• Comprehensive Coverage: Explores association schemes, extremal problems, combinatorial geometries, matroids, and design theory in one cohesive volume.
• Original Research: All papers contain new findings and fresh perspectives, not mere summaries of existing work.
• Global Perspective: Features Ivanov's survey on Soviet contributions, offering insights from a traditionally underrepresented school of thought.
• Enduring Relevance: The open problems and foundational results continue to inspire contemporary research in combinatorics and related fields.

Inside the Book

Readers will find a carefully curated selection of papers that balance theory with application. The book begins with algebraic combinatorics, focusing on association schemes and their connections to group theory. It then moves into extremal combinatorics, tackling questions about the maximum size of set systems with given properties. The final section on metric combinatorics delves into distance-regular graphs and related structures. Each paper is self-contained, with clear definitions and proofs, making the material accessible to motivated graduate students.

Key Topics

• Association schemes and their algebraic properties
• Extremal problems for hypergraphs and set systems
• Combinatorial geometries and matroid theory
• Design theory, including block designs and finite geometries
• Distance-regular graphs and metric spaces
• Applications of linear algebra in combinatorics
• Open problems and conjectures for future research

Reader Benefits

• Deepen Your Understanding: Gain a solid grasp of three core areas of combinatorics through well-written, original papers.
• Research Ready: The open problems and survey sections provide excellent starting points for thesis work or independent study.
• Historical Context: Understand how combinatorial thinking evolved in the 1980s, with insights that remain valuable today.
• Indian Curriculum Alignment: Suitable for advanced undergraduate and postgraduate courses in discrete mathematics, combinatorics, and graph theory offered in Indian universities.

Learning Outcomes

By engaging with this book, readers will be able to: analyze association schemes using algebraic methods; identify extremal configurations in set systems; apply matroid theory to combinatorial optimization; evaluate design theory constructions; and recognize open problems that drive current research. The book also enhances skills in reading and critiquing original research papers, a critical ability for any aspiring mathematician.

Who Should Read

• Graduate Students in mathematics, especially those specializing in combinatorics, discrete mathematics, or theoretical computer science.
• Research Mathematicians seeking a comprehensive reference or inspiration for new problems.
• Faculty Members teaching advanced courses in combinatorics or related fields in Indian colleges and universities.
• Self-learners with a strong background in linear algebra, group theory, and basic combinatorics who wish to explore advanced topics.

About the Author

M. Deza is a distinguished mathematician known for his pioneering contributions to combinatorial theory, particularly in metric combinatorics and extremal problems. With decades of research and editorial experience, Deza has shaped the landscape of modern combinatorics. His work continues to influence scholars worldwide, and this volume reflects his commitment to fostering collaborative research across borders.

About the Publisher

Cambridge University Press is one of the oldest and most respected academic publishers in the world. With a legacy of disseminating high-quality research, Cambridge ensures that each volume meets rigorous scholarly standards. This hardcover edition is built to last, making it a durable companion for years of study and reference.

Conclusion

Algebraic, Extremal and Metric Combinatorics 1986 is more than a conference proceedings—it is a time capsule of mathematical discovery and a toolkit for future innovation. Whether you are a student embarking on research or a seasoned mathematician seeking fresh perspectives, this book offers lasting value. Order your copy today from Bookshops.in and add a classic work to your collection that bridges the past and future of combinatorial science.