点击选择搜索分类
首页 - 小说- 正文
☆☆☆☆☆
||
[美] 米勒(Miller E.) 著
出版社: 世界图书出版公司 ISBN:9787506283045 版次:1 商品编码:10758763 包装:平装 开本:24开 出版时间:2007-10-01 用纸:胶版纸 页数:417
I Monomial Ideals
1 Squarefree monomial ideals
1.1 Equivalent descriptions
1.2 Hilbert series
1.3 Simplicial complexes and homology
1.4 Monomial matrices
1.5 Betti numbers
Exercises
Notes
2 Borel-fixed monomial ideals
2.1 Group actions
2.2 Generic initial ideals
2.3 The Eliahou-Kervaire resolution
2.4 Lex-segment ideals
Exercises
Notes
3 Three-dimensional staircases
3.1 Monomial ideals in two variables
3.2 An example with six monomials.
3.3 The Buchberger graph
3.4 Genericity and deformations...
3.5 The planar resolution algorithm.
Exercises
Notes
4 Cellular resolutions
4.1 Construction and exactness
4.2 Betti numbers and K-polynomials
4.3 Examples of cellular resolutions
4.4 The hull resolution
4.5 Subdividing the simplex
Exercises
Notes
5 Alexander duality
5.1 Simplicial Alexander duality
5.2 Generators versus irreducible components.
5.3 Duality for resolutions
5.4 Cohull resolutions and other applications
5.5 Projective dimension and regular!ty
Exercises
Notes
6 Generic monomial ideals
6.1 Taylor complexes and genericity
6.2 The Scarf complex
6.3 Genericity by deformation
6.4 Bounds on Betti numbers
6.5 Cogeneric monomial ideals
Exercises
Notes
II Toric Algebra
7 Semigroup rings
7.1 Semigroups and lattice ideals
7.2 Affine semigroups and polyhedral cones
7.3 Hilbert bases
7.4 Initial ideals of lattice ideals
Exercises
Notes
8 Multigraded polynomial rings
8.1 Multigradings
8.2 Hilbert series and K-polynomials
8.3 Multigraded Betti numbers
8.4 K-polynomials in nonpositive gradings
8.5 Multidegrees
Exercises
Notes
9 Syzygies of lattice ideals
9.1 Betti numbers
9.2 Laurent monomial modules
9.3 Free resolutions of lattice ideals
9.4 Genericity and the Scarf complex
Exercises
Notes
……
III Determinants
References
Glossary of notation
Index
组合交换代数 电子书 下载 mobi epub pdf txt
组合交换代数-so88
组合交换代数 pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] 米勒(Miller E.) 著
出版社: 世界图书出版公司 ISBN:9787506283045 版次:1 商品编码:10758763 包装:平装 开本:24开 出版时间:2007-10-01 用纸:胶版纸 页数:417
内容简介
The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geometry, graph theory, integer programming, symbolic computation, and statistics. The purpose of this volume is to provide a selfcontained introduction to some of the resulting combinatorial techniques for dealing with polynomial rings, semigroup rings, and determinantal rings.Our exposition mainly concerns combinatorially defined ideals and their quotients, with a focus on numerical invariants and resolutions, especially under gradings more refined than the standard integer grading.目录
PrefaceI Monomial Ideals
1 Squarefree monomial ideals
1.1 Equivalent descriptions
1.2 Hilbert series
1.3 Simplicial complexes and homology
1.4 Monomial matrices
1.5 Betti numbers
Exercises
Notes
2 Borel-fixed monomial ideals
2.1 Group actions
2.2 Generic initial ideals
2.3 The Eliahou-Kervaire resolution
2.4 Lex-segment ideals
Exercises
Notes
3 Three-dimensional staircases
3.1 Monomial ideals in two variables
3.2 An example with six monomials.
3.3 The Buchberger graph
3.4 Genericity and deformations...
3.5 The planar resolution algorithm.
Exercises
Notes
4 Cellular resolutions
4.1 Construction and exactness
4.2 Betti numbers and K-polynomials
4.3 Examples of cellular resolutions
4.4 The hull resolution
4.5 Subdividing the simplex
Exercises
Notes
5 Alexander duality
5.1 Simplicial Alexander duality
5.2 Generators versus irreducible components.
5.3 Duality for resolutions
5.4 Cohull resolutions and other applications
5.5 Projective dimension and regular!ty
Exercises
Notes
6 Generic monomial ideals
6.1 Taylor complexes and genericity
6.2 The Scarf complex
6.3 Genericity by deformation
6.4 Bounds on Betti numbers
6.5 Cogeneric monomial ideals
Exercises
Notes
II Toric Algebra
7 Semigroup rings
7.1 Semigroups and lattice ideals
7.2 Affine semigroups and polyhedral cones
7.3 Hilbert bases
7.4 Initial ideals of lattice ideals
Exercises
Notes
8 Multigraded polynomial rings
8.1 Multigradings
8.2 Hilbert series and K-polynomials
8.3 Multigraded Betti numbers
8.4 K-polynomials in nonpositive gradings
8.5 Multidegrees
Exercises
Notes
9 Syzygies of lattice ideals
9.1 Betti numbers
9.2 Laurent monomial modules
9.3 Free resolutions of lattice ideals
9.4 Genericity and the Scarf complex
Exercises
Notes
……
III Determinants
References
Glossary of notation
Index
前言/序言
组合交换代数 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 无痕山林
- 实用冲压工艺及模具设计手册
- 探险者发现之旅丛书:征服冰峰之旅
- 异步电机无速度传感器高性能控制技术
- 科学探索与发现系列 失落的文明 杨江华
- 铸造手册(第2卷):铸钢(第3版)
- {RT}破译者:从古埃及法老到量子时代的密码史:the history of code a
- 典型零件机械加工生产实例 第3版
- (青少年“海洋梦”系列丛书)凌波踏浪——航海设备与舰只
- 认识我看透他
- 神奇的太空
- 9787551105781 奶嘴男,怎么爱 花山文艺出版社 莫哆
- 幻想的奇迹:技术发明99
- 电工电子学(第四版)学习辅导与习题解答/“十二五”普通高等教育本科国家级规划教材
- 乔托的几何学遗产:科学革命前夕的美术与科学(何香凝美术馆 艺术史名著译丛) [美]小塞缪