作者：(美) 贝拉·巴伊诺克
页数：408
出版社：哈尔滨工业大学出版社
出版日期：2023
ISBN：9787576706277
电子书格式：pdf/epub/txt
内容简介
本书是一本关于结构的英文版数学专著。本书的主题是加性组合学—一个现代数学研究的领域.加性组合学一是组合数论和加性数论的产物——可以被描述为对加性结构中和集(带有给定子集项的和的集合)的组合性质的研究。在本书中，我们解释了加性组合学，从狭义的角度来说，比如对有限阿贝尔群中的和集的研究.（目前我们对第二卷内容的计划是集中于对整数集和其他有限群的研究.)本书为在该领域中对调查研究感兴趣的任何学生提供了可以进行广泛研究的项目选择列表。
作者简介
贝拉·巴伊诺克教授是美国盖茨堡学院的数学教授和校友会主席。他从俄亥俄州立大学获得了博士学位，并获得了很多教学奖，包括在盖茨堡学院获得的有创造性的教学奖，以及在美国数学协会获得的克劳福德教学奖。
目录
Preface
Notations
I Ingredients
1 Number theory
1.1 Divisibility of integers
1.2 Congruences
1.3 The Fundamental Theorem of Number Theory
1.4 Multiplicative number theory
1.5 Additive number theory
2 Combinatorics
2.1 Basic enumeration principles
2.2 Counting lists, sequences, sets, and multisets
2.3 Binomial coefficients and Pascal’s Triangle
2.4 Some recurrence relations
2.5 The integer lattice and its layers
3 Group theory
3.1 Finite abelian groups
3.2 Group isomorphisms
3.3 The Fundamental Theorem of Finite Abelian Groups
3.4 Subgroups and cosets
3.5 Subgroups generated by subsets
3.6 Sumsets
II Appetizers
Spherical designs
Caps, centroids, and the game SET
How many elements does it take to span a group?
In pursuit of perfection
The declaration of independence
III Sides
The function vg (n, h)
The function v+(n, h)
The function u(n, m, h)
The function u^(n, m, h)
IV Entrees
A Maximum sumset size
A.1 Unrestricted sumsets
A.1.1 Fixed number of terms
A.1.2 Limited number of terms
A.1.3 Arbitrary number of terms
A.2 Unrestricted signed sumsets
A.2.1 Fixed number of terms
A.2.2 Limited number of terms
A.2.3 Arbitrary numbcr of terms
A.3 Restricted sumsets
A.3.1 Fixed number of terms
A.3.2 Limited number of terms
A.3.3 Arbitrary number of terms
A.4 Restricted signed sumscts
A.4.1 Fixed number of terms
A.4.2 Limited number of terms
Notations
I Ingredients
1 Number theory
1.1 Divisibility of integers
1.2 Congruences
1.3 The Fundamental Theorem of Number Theory
1.4 Multiplicative number theory
1.5 Additive number theory
2 Combinatorics
2.1 Basic enumeration principles
2.2 Counting lists, sequences, sets, and multisets
2.3 Binomial coefficients and Pascal’s Triangle
2.4 Some recurrence relations
2.5 The integer lattice and its layers
3 Group theory
3.1 Finite abelian groups
3.2 Group isomorphisms
3.3 The Fundamental Theorem of Finite Abelian Groups
3.4 Subgroups and cosets
3.5 Subgroups generated by subsets
3.6 Sumsets
II Appetizers
Spherical designs
Caps, centroids, and the game SET
How many elements does it take to span a group?
In pursuit of perfection
The declaration of independence
III Sides
The function vg (n, h)
The function v+(n, h)
The function u(n, m, h)
The function u^(n, m, h)
IV Entrees
A Maximum sumset size
A.1 Unrestricted sumsets
A.1.1 Fixed number of terms
A.1.2 Limited number of terms
A.1.3 Arbitrary number of terms
A.2 Unrestricted signed sumsets
A.2.1 Fixed number of terms
A.2.2 Limited number of terms
A.2.3 Arbitrary numbcr of terms
A.3 Restricted sumsets
A.3.1 Fixed number of terms
A.3.2 Limited number of terms
A.3.3 Arbitrary number of terms
A.4 Restricted signed sumscts
A.4.1 Fixed number of terms
A.4.2 Limited number of terms
