Algebraic combinatorics. Translated from the Japanese
type: Item
instance of: scholarly article
title: Algebraic combinatorics. Translated from the Japanese
zbMATH Open document ID: 1472.05002
DOI: 10.1515/9783110630251
author: Eiichi Bannai
author: Etsuko Bannai
author: Tatsuro Ito
author: Rie Tanaka
published in: De Gruyter Series in Discrete Mathematics and Applications
publication date: 2020-12-01T00:00:00Z
review text: 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.
reviewed by: Andrés R. Vindas Meléndez
Mathematics Subject Classification ID: 05-01
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 7279831
zbMATH Keywords: algebraic combinatorics
zbMATH Keywords: association schemes
zbMATH Keywords: coding theory
zbMATH Keywords: spheres
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110630251
OpenAlex ID: W4239024445
description: scientific article