作者Bruce E. Sagan 编
出版社世界图书出版公司
出版时间2012-06
版次2
装帧平装
货号A6
上书时间2024-12-24
商品详情
- 品相描述:九品
图书标准信息
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作者
Bruce E. Sagan 编
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出版社
世界图书出版公司
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出版时间
2012-06
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版次
2
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ISBN
9787510044021
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定价
45.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
238页
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正文语种
英语
- 【内容简介】
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《对称群(第2版)》是一部研究生教程,几乎囊括了该领域的重要结果,是经典中的经典。书中包括了很多新资料,例如,hook公式的novelli-pak-stoyanovskii证明,运用偏微分部分有序集的平方和证明,平方和公式的fomin双射证明,部分有序集上的群行为及其在单峰性证明中应用和色对称函数。
- 【目录】
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prefacetothe2ndedition
prefacetothe1steition
1grouprepresentations
1.1fundamentalconcepts
1.2matrixrepresentations
1.3g-modulesandthegroupalgebra
1.4reducibility
1.5completereducibilityandmaschke'stheorem
1.6g-homomorphismsandschur'slemma
1.7commutantandendomorphismalgebras
1.8groupcharacters
1.9innerproductsofcharacters
1.10decompositionofthegroupalgebra
1.11tensorproductsagain
1.12restrictedandinducedrepresentations
1.13exercises
2representationsofthesymmetricgroup
2.1youngsubgroups,tableaux,andtabloids
2.2dominanceandlexicographicordering
2.3spechtmodules
2.4thesubmoduletheorem
2.5standardtableauxandabasisfors
2.6garnirelements
2.7young'snaturalrepresentation
2.8thebranchingrule
2.9thedecompositionofmy
2.10thesemistandardbasisforhom(s,m)
2.11kostkanumbersandyoung'srule
2.12exercises
3combinatorialalgorithms
3.1therobinson-schenstedalgorithm
3.2columninsertion
3.3increasinganddecreasingsubsequences
3.4theknuthrelations
3.5subsequencesagain
3.6viennot'sgeometricconstruction
3.7schutzenberger'sjeudetaquin
3.8dualequivalence
3.9evacuation
3.10thehookformula
3.11thedeterminantalformula
3.12exercises
4symmetricfunctions
4.1introductiontogeneratingfunctions
4.2thehillman-grasslalgorithm
4.3theringofsymmetricfunctions
4.4schurfunctions
4.5thejacobi-trudideterminants
4.6otherdefinitionsoftheschurfunction
4.7thecharacteristicmap
4.8knuth'salgorithm
4.9thelittlewood-richardsonrule
4.10themurnnghan-nakayamarule
4.11exercises
5applicationsandgeneralizations
5.1young'slatticeanddifferentialposets
5.2growthsandlocalrules
5.3groupsactingonposets
5.4unimodality
5.5chromaticsymmetricfunctions
5.6exercises
bibliography
index
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