Symmetric Functions And Hall Polynomials
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Symmetric Functions And Hall Polynomials
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Author : Ian Grant Macdonald
language : en
Publisher: Oxford University Press
Release Date : 1998
Symmetric Functions And Hall Polynomials written by Ian Grant Macdonald and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This is a paperback version of the second, much expanded, edition of Professor Macdonald's acclaimed monograph on symmetric functions and Hall polynomials. Almost every chapter has new sections and new examples have been included throughout. Extra material in the appendix to Chapter 1, for example, includes an account of the related theory of polynomial representations of the general linear groups (always in characteristic zero). Chapters 6 and 7 are new to the second edition: Chapter 6 contains an extended account of a family of symmetric functions depending rationally on two parameters. These symmetric functions include as particular cases many of those encountered earlier in the book but they also include, as a limiting case, Jack's symmetric functions depending on a parameter (. Many of the properties of the Schur functions generalize to these two-parameter symmetric functions, but the proofs (at present) are usually more elaborate. Chapter 7 is devoted to the study of the zonal polynomials, long familiar to statisticians. From one point of view they are a special case of Jack's symmetric functions (the parameter ( being equal to 2) but their combinatorial and group-theoretic connections make them worthy of study in their own right. From reviews of the first edition: 'Despite the amount of material of such great potential interest to mathematicians...the theory of symmetric functions remains all but unknown to the persons it is most likely to benefit...Hopefully this beautifully written book will put an end to this state of affairs...I have no doubt that this book will become the definitive reference on symmetric functions and their applications.' Bulletin of the AMS '...In addition to providing a self-contained and coherent account of well-known and classical work, there is a great deal which is original. The book is dotted with gems, both old and new...It is a substantial and valuable volume and will be regarded as the authoritative source which has been long awaited in this subject.' LMS book reviews From reviews of the second edition: 'Evidently this second edition will be the source and reference book for symmetric functions in the near future.'Zbl. Math.
Symmetric Functions And Hall Polynomials
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Author : I. G. Macdonald
language : en
Publisher:
Release Date : 1979
Symmetric Functions And Hall Polynomials written by I. G. Macdonald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Abelian groups categories.
The Q T Catalan Numbers And The Space Of Diagonal Harmonics
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Author : James Haglund
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
The Q T Catalan Numbers And The Space Of Diagonal Harmonics written by James Haglund and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.
The Symmetric Group
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Author : Bruce E. Sagan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Symmetric Group written by Bruce E. Sagan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
I have been very gratified by the response to the first edition, which has resulted in it being sold out. This put some pressure on me to come out with a second edition and now, finally, here it is. The original text has stayed much the same, the major change being in the treatment of the hook formula which is now based on the beautiful Novelli-Pak-Stoyanovskii bijection (NPS 97]. I have also added a chapter on applications of the material from the first edition. This includes Stanley's theory of differential posets (Stn 88, Stn 90] and Fomin's related concept of growths (Fom 86, Fom 94, Fom 95], which extends some of the combinatorics of Sn-representations. Next come a couple of sections showing how groups acting on posets give rise to interesting representations that can be used to prove unimodality results (Stn 82]. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta]. I would like to thank all the people, too numerous to mention, who pointed out typos in the first edition. My computer has been severely reprimanded for making them. Thanks also go to Christian Krattenthaler, Tom Roby, and Richard Stanley, all of whom read portions of the new material and gave me their comments. Finally, I would like to give my heartfelt thanks to my editor at Springer, Ina Lindemann, who has been very supportive and helpful through various difficult times.
Young Tableaux
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Author : William Fulton
language : en
Publisher: Cambridge University Press
Release Date : 1997
Young Tableaux written by William Fulton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.
Affine Hecke Algebras And Orthogonal Polynomials
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Author : I. G. Macdonald
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-20
Affine Hecke Algebras And Orthogonal Polynomials written by I. G. Macdonald and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-20 with Mathematics categories.
First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Symmetric Functions And Orthogonal Polynomials
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Author : Ian Grant Macdonald
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Symmetric Functions And Orthogonal Polynomials written by Ian Grant Macdonald and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials, has long been known to be connected to combinatorics, representation theory and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Symmetric Functions And Combinatorial Operators On Polynomials
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Author : Alain Lascoux
language : en
Publisher: American Mathematical Soc.
Release Date :
Symmetric Functions And Combinatorial Operators On Polynomials written by Alain Lascoux and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
The theory of symmetric functions is an old topic in mathematics which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and itsoccurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independentchapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods or the method of Cauchy. The last chapter sketches a non-commutative version of symmetric functions, using Young tableaux and the plactic monoid. The book contains numerous exercises clarifying and extending many points of the main text. It will make an excellent supplementary text for a graduate course in combinatorics.
Symmetric Functions 2001 Surveys Of Developments And Perspectives
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Author : Sergey Fomin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetric Functions 2001 Surveys Of Developments And Perspectives written by Sergey Fomin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Study Institute, held in Cambridge, UK, from 25th June to 6th July, 2001