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對稱群(第2版)的圖書 |
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對稱群-第2版 作者：薩根 出版社：世界圖書(北京)出版公司 出版日期：2012-06-01 語言：簡體書 |
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| 型式 | 價格 | 供應商 | 所屬目錄 | $ 238 |
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圖書介紹 - 資料來源：博客來 評分：
圖書名稱：對稱群(第2版)
內容簡介
是一部研究生教程，幾乎囊括了該領域的重要結果，是經典中的經典。書中包括了很多新資料，例如hook公式的novelli-pak-stoyanovskii證明，運用偏微分部分有序集的平方和證明，平方和公式的fomin雙射證明，部分有序集上的群行為及其在單峰性證明中應用和色對稱函數。
目錄
Preface to the 2nd Edition
Preface to the 1st Eition
1 Group Representations
1.1 Fundamental Concepts
1.2 Matrix Representations
1.3 G-Modules and the Group Algebra
1.4 Reducibility
1.5 Complete Reducibility and Maschke’’s Theorem
1.6 G-Homomorphisms and Schur’’s Lemma
1.7 Commutant and Endomorphism Algebras
1.8 Group Characters
1.9 Inner Products of Characters
1.10 Decomposition of the Group Algebra
1.11 Tensor Products Again
1.12 Restricted and Induced Representations
1.13 Exercises
2 Representations of the Symmetric Group
2.1 Young Subgroups, Tableaux, and Tabloids
2.2 Dominance and Lexicographic Ordering
2.3 Specht Modules
2.4 The Submodule Theorem
2.5 Standard Tableaux and a Basis for S λ
2.6 Garnir Elements
2.7 Young’’s Natural Representation
2.8 The Branching Rule
2.9 The Decomposition of Mμ
2.10 The Semistandard Basis for Hom（Sλ, Mμ）
2.11 Kostka Numbers and Young’’s Rule
2.12 Exercises
Combinatorial Algorithms
3.1 The Robinson-Schensted Algorithm
3.2 Column Insertion
3.3 Increasing and Decreasing Subsequences
3.4 The Knuth Relations
3.5 Subsequences Again
3.6 Viennot’’s Geometric Construction
3.7 Schùtzenberger’’s Jeu de Taquin
3.8 Dual Equivalence
3.9 Evacuation
3.10 The Hook Formula
3.11 The Determinantal Formula
3.12 Exercises
4 Symmetric Functions
4.1 Introduction to Generating Functions
4.2 The Hillman-Grassl Algorithm
4.3 The Ring of Symmetric Functions
4.4 Schur Functions
4.5 The Jacobi-Trudi Determinants
4.6 Other Definitions of the Schur Function
4.7 The Characteristic Map
4.8 Knuth’’s Algorithm
4.9 The Littlewood-Richardson Rule
4.10 The Murnaghan-Nakayama Rule
4.11 Exercises
5 Applications and Generalizations
5.1 Young’’s Lattice and Differential Posets.
5.2 Growths and Local Rules
5.3 Groups Acting on Posets
5.4 Unimodality
5.5 Chromatic Symmetric Functions
5.6 Exercises
Bibliography
Index
Preface to the 1st Eition
1 Group Representations
1.1 Fundamental Concepts
1.2 Matrix Representations
1.3 G-Modules and the Group Algebra
1.4 Reducibility
1.5 Complete Reducibility and Maschke’’s Theorem
1.6 G-Homomorphisms and Schur’’s Lemma
1.7 Commutant and Endomorphism Algebras
1.8 Group Characters
1.9 Inner Products of Characters
1.10 Decomposition of the Group Algebra
1.11 Tensor Products Again
1.12 Restricted and Induced Representations
1.13 Exercises
2 Representations of the Symmetric Group
2.1 Young Subgroups, Tableaux, and Tabloids
2.2 Dominance and Lexicographic Ordering
2.3 Specht Modules
2.4 The Submodule Theorem
2.5 Standard Tableaux and a Basis for S λ
2.6 Garnir Elements
2.7 Young’’s Natural Representation
2.8 The Branching Rule
2.9 The Decomposition of Mμ
2.10 The Semistandard Basis for Hom（Sλ, Mμ）
2.11 Kostka Numbers and Young’’s Rule
2.12 Exercises
Combinatorial Algorithms
3.1 The Robinson-Schensted Algorithm
3.2 Column Insertion
3.3 Increasing and Decreasing Subsequences
3.4 The Knuth Relations
3.5 Subsequences Again
3.6 Viennot’’s Geometric Construction
3.7 Schùtzenberger’’s Jeu de Taquin
3.8 Dual Equivalence
3.9 Evacuation
3.10 The Hook Formula
3.11 The Determinantal Formula
3.12 Exercises
4 Symmetric Functions
4.1 Introduction to Generating Functions
4.2 The Hillman-Grassl Algorithm
4.3 The Ring of Symmetric Functions
4.4 Schur Functions
4.5 The Jacobi-Trudi Determinants
4.6 Other Definitions of the Schur Function
4.7 The Characteristic Map
4.8 Knuth’’s Algorithm
4.9 The Littlewood-Richardson Rule
4.10 The Murnaghan-Nakayama Rule
4.11 Exercises
5 Applications and Generalizations
5.1 Young’’s Lattice and Differential Posets.
5.2 Growths and Local Rules
5.3 Groups Acting on Posets
5.4 Unimodality
5.5 Chromatic Symmetric Functions
5.6 Exercises
Bibliography
Index
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