Symmetric Functions And Combinatorial Operators On Polynomials

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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 And Combinatorial Operators On Polynomials

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Author : Alain Lascoux
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

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 2003 with Mathematics 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 its occurrence 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 independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods, or the method of Cauchy and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.

Symmetric Functions And Combinatorial Operators On Polynomials

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Author : Alain Lascoux
language : en
Publisher:
Release Date : 2003

Symmetric Functions And Combinatorial Operators On Polynomials written by Alain Lascoux and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with 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.

Algorithmic Combinatorics Enumerative Combinatorics Special Functions And Computer Algebra

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Author : Veronika Pillwein
language : en
Publisher: Springer Nature
Release Date : 2020-09-28

Algorithmic Combinatorics Enumerative Combinatorics Special Functions And Computer Algebra written by Veronika Pillwein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Computers categories.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

Zeta And L Functions In Number Theory And Combinatorics

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Author : Wen-Ching Winnie Li
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-01

Zeta And L Functions In Number Theory And Combinatorics written by Wen-Ching Winnie Li 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 2019-03-01 with Mathematics categories.

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

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.

Bounded Littlewood Identities

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Author : Eric M. Rains
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21

Bounded Littlewood Identities written by Eric M. Rains 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 2021-07-21 with Education categories.

We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.

Algebraic Cycles Sheaves Shtukas And Moduli

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Author : Piotr Pragacz
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-12

Algebraic Cycles Sheaves Shtukas And Moduli written by Piotr Pragacz 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 2008-03-12 with Mathematics categories.

Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.

Numerical Methods For Structured Matrices And Applications

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Author : Dario Andrea Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-09

Numerical Methods For Structured Matrices And Applications written by Dario Andrea Bini 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 2011-02-09 with Mathematics categories.

This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.