An Introduction To Symmetric Functions And Their Combinatorics
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An Introduction To Symmetric Functions And Their Combinatorics
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Author : Eric S. Egge
language : en
Publisher:
Release Date : 1920
An Introduction To Symmetric Functions And Their Combinatorics written by Eric S. Egge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1920 with Combinatorial analysis categories.
This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution \omega; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, i.
An Introduction To Symmetric Functions And Their Combinatorics
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Author : Eric S. Egge
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-18
An Introduction To Symmetric Functions And Their Combinatorics written by Eric S. Egge 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 2019-11-18 with Education categories.
This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.
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.
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.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet 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 2009-01-15 with Mathematics categories.
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Analysis And Linear Algebra The Singular Value Decomposition And Applications
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Author : James Bisgard
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-19
Analysis And Linear Algebra The Singular Value Decomposition And Applications written by James Bisgard 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 2020-10-19 with Education categories.
This book provides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear algebra to data science. Four important applications relevant to data science are considered throughout the book: determining the subspace that “best” approximates a given set (dimension reduction of a data set); finding the “best” lower rank approximation of a given matrix (compression and general approximation problems); the Moore-Penrose pseudo-inverse (relevant to solving least squares problems); and the orthogonal Procrustes problem (finding the orthogonal transformation that most closely transforms a given collection to a given configuration), as well as its orientation-preserving version. The point of view throughout is analytic. Readers are assumed to have had a rigorous introduction to sequences and continuity. These are generalized and applied to linear algebraic ideas. Along the way to the SVD, several important results relevant to a wide variety of fields (including random matrices and spectral graph theory) are explored: the Spectral Theorem; minimax characterizations of eigenvalues; and eigenvalue inequalities. By combining analytic and linear algebraic ideas, readers see seemingly disparate areas interacting in beautiful and applicable ways.
Galois Theory For Beginners A Historical Perspective Second Edition
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-15
Galois Theory For Beginners A Historical Perspective Second Edition written by Jörg Bewersdorff 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 2021-07-15 with Education categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Symmetric Functions A Beginner S Course
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Author : Evgeny Smirnov
language : en
Publisher: Springer Nature
Release Date : 2024-06-07
Symmetric Functions A Beginner S Course written by Evgeny Smirnov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-07 with Mathematics categories.
This book is devoted to combinatorial aspects of the theory of symmetric functions. This rich, interesting and highly nontrivial part of algebraic combinatorics has numerous applications to algebraic geometry, topology, representation theory and other areas of mathematics. Along with classical material, such as Schur polynomials and Young diagrams, less standard subjects are also covered, including Schubert polynomials and Danilov–Koshevoy arrays. Requiring only standard prerequisites in algebra and discrete mathematics, the book will be accessible to undergraduate students and can serve as a basis for a semester-long course. It contains more than a hundred exercises of various difficulty, with hints and solutions. Primarily aimed at undergraduate and graduate students, it will also be of interest to anyone who wishes to learn more about modern algebraic combinatorics and its usage in other areas of mathematics.
Stochastic Differential Equations For Chemical Transformations In White Noise Probability Space
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Author : Don Kulasiri
language : en
Publisher: Springer Nature
Release Date : 2025-01-27
Stochastic Differential Equations For Chemical Transformations In White Noise Probability Space written by Don Kulasiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Science categories.
This book highlights the applications of stochastic differential equations in white noise probability space to chemical reactions that occur in biology. These reactions operate in fluctuating environments and are often coupled with each other. The theory of stochastic differential equations based on white noise analysis provides a physically meaningful modelling framework. The Wick product-based calculus for stochastic variables is similar to regular calculus; therefore, there is no need for Ito calculus. Numerical examples are provided with novel ways to solve the equations. While the theory of white noise analysis is well developed by mathematicians over the past decades, applications in biophysics do not exist. This book provides a bridge between this kind of mathematics and biophysics.
The Great Prime Number Race
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Author : Roger Plymen
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-13
The Great Prime Number Race written by Roger Plymen 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 2020-08-13 with Education categories.
Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.