Algebraic combinatorics. Translated from the Japanese
This book is the English translation of the book Introduction to Algebraic Combinatorics, which was published by Kyoritsu Shuppan in 2016 and written by the first three authors in Japanese. Later, the fourth author joined the team and translated the book in its current form in English. Bannai and Ito describe algebraic combinatorics as ``a group theory without groups'' or ``a character theoretical study of combinatorial objects''. The aim of this book is to ``pursue the study of combinatorics as an extension or a generalization of the study of finite permutation groups''. The early chapters of the book provides an accessible introduction to the subject for undergraduates and interested readers. The later chapters are suited for researchers in combinatorics and broader areas. Chapter 1 is an introduction to classical combinatorics with selected subjects of study, such as graph theory and coding theory. Chapter 2 is an introduction to association schemes. Chapter 3 and 4 present codes and designs in connection to association schemes. Chapter 5 is on algebraic combinatorics on spheres. The book ends with Chapter 6 covering \(P\) and \(Q\)-polynomial schemes.
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