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內容簡介

《對稱群（第2版）》是一部研究生教程，幾乎囊括瞭該領域的重要結果，是經典中的經典。書中包括瞭很多新資料，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。

內頁插圖

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
2.6 garnir elements
2.7 young's natural representation
2.8 the branching rule
2.9 the decomposition of my
2.10 the semistandard basis for hom（s, m）
2.11 kostka numbers and young's rule
2.12 exercises

3 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 schutzenberger'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 murnnghan-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

前言/序言

對稱群（第2版） 下載 mobi epub pdf txt 電子書

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好。字數補丁

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joli

評分☆☆☆☆☆

這是經典的關於對稱群的書，無需多言，非常好。

評分☆☆☆☆☆

好。字數補丁

評分☆☆☆☆☆

好。字數補丁

評分☆☆☆☆☆

joli

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典型的數學書，不適閤物理係的人

評分☆☆☆☆☆

好。字數補丁

評分☆☆☆☆☆

joli

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