Algebraic Combinatorics最新文献

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Preface 前言
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-201
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引用次数: 0
4 Codes and designs in association schemes (continued) 4关联方案中的规范和设计(续)
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-004
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引用次数: 0
3 Codes and designs in association schemes (Delsarte theory on association schemes) 3关联方案中的代码和设计(Delsarte关联方案理论)
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-003
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引用次数: 0
Preface to the Japanese version 日文版前言
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-202
E. Bannai
{"title":"Preface to the Japanese version","authors":"E. Bannai","doi":"10.1515/9783110630251-202","DOIUrl":"https://doi.org/10.1515/9783110630251-202","url":null,"abstract":"The purpose of this book is to give an introduction to algebraic combinatorics. There is no explicit definition of algebraic combinatorics. In Algebraic Combinatorics I (1984), written by Eiichi Bannai and Tatsuro Ito, algebraic combinatorics is described as “a group theorywithout groups” or “a character theoretical study of combinatorial objects.” Specifically speaking, we pursue the study of combinatorics as an extension or a generalization of the study of finite permutation groups. In this book, we keep this direction in our mind. This is also the approach, initiated by Philippe Delsarte, which enables us to look at a wide range of combinatorial objects such as graphs, codes, and designs from a unified viewpoint. Based on these thoughts, we explain Delsarte’s theory and its various extensions. When we finished writing Algebraic Combinatorics I, we wanted to write the sequel Algebraic Combinatorics II soon. We regret we did not write it up at that time, but due to various reasons, we could not. We would not say that it has nothing to do with our laziness, but if we could use an excuse, it seems that the developments in the field are not enough to complete a book, and the range of mathematical objects that we are interested in has expanded too widely to handle. Therefore, we thought we could and should write on algebraic combinatorics on spheres, and in 1999, Eiichi Bannai and Etsuko Bannai published Algebraic Combinatorics on Spheres, written in Japanese. We did not prepare an English edition because we planned to write Algebraic Combinatorics II in the future, and we regard the above book as a preparation for it. In the present book, we want to present another subject, Delsarte’s theory in association schemes. Besides, we would like to start writing on the classification of Pand Q-polynomial association schemes, which is themost important problem in Algebraic Combinatorics I, through the study of Terwilliger algebras by Terwilliger and Ito. In this sense, writing up this book enabled us to work seriously on Algebraic Combinatorics II. Before we know it, we get older. Counting the remaining time in our lives, we would like to write one more work. We give an overview on the contents of this book in the following. Chapter 1 is the introduction to classical combinatorics. The contents are suitable for undergraduate courses. In Japan, there are not so many universities offering lectures on combinatorics for undergraduates. Therefore, we selected basic subjects which beginners in combinatorics should learn. The contents are slightly long for a one-semester course. Chapter 2 is the introduction to association schemes. Some contents overlap with Algebraic Combinatorics I (and with Algebraic Combinatorics on Spheres). We start with the basics, so the chapter is comprehensive for readers who are not familiar with this area. Chapter 3 is the introduction to Delsarte’s theory, which is the theory of codes and designs in association schemes. The descriptio","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/9783110630251-202","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48407228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Inclusion-exclusion on Schubert polynomials 舒伯特多项式的包容-排斥
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.5802/alco.200
Karola M'esz'aros, Arthur Tanjaya
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引用次数: 4
1 Classical design theory and classical coding theory 1经典设计理论和经典编码理论
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-001
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引用次数: 0
2 Association schemes 2协会计划
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-002
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引用次数: 0
5 Algebraic combinatorics on spheres and general remarks on algebraic combinatorics 5球上的代数组合及代数组合的一般注释
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-005
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引用次数: 0
Bibliography 参考书目
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-007
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引用次数: 0
Frontmatter
Algebraic Combinatorics Pub Date : 2021-02-22 DOI: 10.1515/9783110630251-fm
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引用次数: 0
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