Current Trends In Symmetric Polynomials With Their Applications

Author : Taekyun Kim
Publisher : MDPI
Page : 206 pages
File Size : 53,8 Mb
Release : 2021-03-19
Category : Mathematics
ISBN : 9783036503608

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Current Trends in Symmetric Polynomials with Their Applications Ⅱ by Taekyun Kim Pdf

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Author : Taekyun Kim
Publisher : MDPI
Page : 238 pages
File Size : 40,8 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783039216208

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Current Trends in Symmetric Polynomials with their Applications by Taekyun Kim Pdf

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Author : Taekyun Kim
Publisher : Unknown
Page : 208 pages
File Size : 54,5 Mb
Release : 2021
Category : Electronic
ISBN : 3036503617

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Current Trends in Symmetric Polynomials with Their Applications II by Taekyun Kim Pdf

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Author : Taekyun Kim
Publisher : Unknown
Page : 1 pages
File Size : 52,5 Mb
Release : 2019
Category : Electronic books
ISBN : 303921621X

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Current Trends in Symmetric Polynomials with Their Applications by Taekyun Kim Pdf

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Author : Alma Adams
Publisher : NY Research Press
Page : 0 pages
File Size : 48,5 Mb
Release : 2023-09-26
Category : Mathematics
ISBN : 1647254620

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Symmetric Functions and Polynomials (Mathematics Essentials) by Alma Adams Pdf

A function containing several variables that remains unchanged for any permutation of the variables is called a symmetric function. Polynomials are a type of function. A symmetric polynomial refers to a type of polynomial P in n variables such that if any of the variables are swapped with each other, it remains the same polynomial. There are various types of symmetric polynomials including power-sum symmetric polynomials, elementary symmetric polynomials, complete homogeneous symmetric polynomials, monomial symmetric polynomials, and Schur polynomials. Symmetric polynomials have numerous applications in various areas of combinatorics, representation theory, mathematical physics, and mathematics. They are frequently found in Newton's identities and Vieta's formula. This book includes some of the vital pieces of works being conducted across the world, on various topics related to symmetric functions and polynomials, and their applications. It will serve as a valuable source of reference for graduate and postgraduate students.

Author : Alain Lascoux
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 41,6 Mb
Release : 2003
Category : Polynomials
ISBN : 9780821828717

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Symmetric Functions and Combinatorial Operators on Polynomials by Alain Lascoux Pdf

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.

Author : Ian Grant Macdonald
Publisher : Oxford University Press, USA
Page : 200 pages
File Size : 41,8 Mb
Release : 1979
Category : Abelian groups
ISBN : UOM:39076006138817

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Symmetric Functions and Hall Polynomials by Ian Grant Macdonald Pdf

This new and much expanded edition of a well-received book remains the only text available on the subject of symmetric functions and Hall polynomials. There are new sections in almost every chapter, and many new examples have been included throughout.

Author : Francisco Marcellán,Edmundo J. Huertas
Publisher : Springer Nature
Page : 327 pages
File Size : 48,7 Mb
Release : 2021
Category : Analysis (Mathematics).
ISBN : 9783030561901

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Orthogonal Polynomials: Current Trends and Applications by Francisco Marcellán,Edmundo J. Huertas Pdf

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganés, Spain, from July 3 to July 6, 2018. These meetings were mainly focused to encourage research in the fields of approximation theory, special functions, orthogonal polynomials and their applications among graduate students as well as young researchers from Latin America, Spain and Portugal. The presentation of the state of the art as well as some recent trends constitute the aim of the lectures delivered in the EIBPOA by worldwide recognized researchers in the above fields. In this volume, several topics on the theory of polynomials orthogonal with respect to different inner products are analyzed, both from an introductory point of view for a wide spectrum of readers without an expertise in the area, as well as the emphasis on their applications in topics as integrable systems, random matrices, numerical methods in differential and partial differential equations, coding theory, and signal theory, among others.

Author : Ian Grant Macdonald
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 51,8 Mb
Release : 1998
Category : Orthogonal polynomials
ISBN : 9780821807705

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Symmetric Functions and Orthogonal Polynomials by Ian Grant Macdonald Pdf

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.

Author : Jeffrey Remmel,Anthony Mendes
Publisher : Birkhäuser
Page : 292 pages
File Size : 45,7 Mb
Release : 2015-11-28
Category : Mathematics
ISBN : 9783319236186

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Counting with Symmetric Functions by Jeffrey Remmel,Anthony Mendes Pdf

This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.

Author : Frank Uhlig,Robert Grone
Publisher : North Holland
Page : 480 pages
File Size : 47,7 Mb
Release : 1987
Category : Matrices
ISBN : UCAL:B4515251

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Current Trends in Matrix Theory by Frank Uhlig,Robert Grone Pdf

This volume contains 41 original papers and 22 abstracts of research in linear algebra and applications currently conducted by many of the leading experts in the field. More than a dozen of the papers are survey articles, while several propose open problems. The applications range from control to probability theory, with strong emphasis on matrix polynomials, Schur complements, permanents, numerical computation, combinatorics, and core linear algebra.

Author : Eric S. Egge
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 49,8 Mb
Release : 2019-11-18
Category : Education
ISBN : 9781470448998

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An Introduction to Symmetric Functions and Their Combinatorics by Eric S. Egge Pdf

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.

Author : Cheon Seoung Ryoo
Publisher : BoD – Books on Demand
Page : 174 pages
File Size : 43,6 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781838802691

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Polynomials by Cheon Seoung Ryoo Pdf

Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Author : Emilio Gómez Déniz
Publisher : MDPI
Page : 146 pages
File Size : 47,9 Mb
Release : 2021-01-21
Category : Social Science
ISBN : 9783039366460

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Symmetric and Asymmetric Distributions by Emilio Gómez Déniz Pdf

In recent years, the advances and abilities of computer software have substantially increased the number of scientific publications that seek to introduce new probabilistic modelling frameworks, including continuous and discrete approaches, and univariate and multivariate models. Many of these theoretical and applied statistical works are related to distributions that try to break the symmetry of the normal distribution and other similar symmetric models, mainly using Azzalini's scheme. This strategy uses a symmetric distribution as a baseline case, then an extra parameter is added to the parent model to control the skewness of the new family of probability distributions. The most widespread and popular model is the one based on the normal distribution that produces the skewed normal distribution. In this Special Issue on symmetric and asymmetric distributions, works related to this topic are presented, as well as theoretical and applied proposals that have connections with and implications for this topic. Immediate applications of this line of work include different scenarios such as economics, environmental sciences, biometrics, engineering, health, etc. This Special Issue comprises nine works that follow this methodology derived using a simple process while retaining the rigor that the subject deserves. Readers of this Issue will surely find future lines of work that will enable them to achieve fruitful research results.

Author : I.M. Gelfand,Vladimir S Retakh
Publisher : Unknown
Page : 128 pages
File Size : 46,5 Mb
Release : 2005-02-01
Category : Electronic
ISBN : 0817638334

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Quasideterminants, Noncommutative Symmetric Functions and Their Applications by I.M. Gelfand,Vladimir S Retakh Pdf