Young Tableaux In Combinatorics Invariant Theory And Algebra

Author : Joseph P.S. Kung
Publisher : Elsevier
Page : 344 pages
File Size : 43,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483272023

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Young Tableaux in Combinatorics, Invariant Theory, and Algebra by Joseph P.S. Kung Pdf

Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians. Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardson rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory. This volume will be helpful to students and practitioners of algebra.

Author : Hélène Barcelo,Gizem Karaali,Rosa Orellana
Publisher : Springer
Page : 362 pages
File Size : 40,9 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030051419

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Recent Trends in Algebraic Combinatorics by Hélène Barcelo,Gizem Karaali,Rosa Orellana Pdf

This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.

Author : Dennis Stanton
Publisher : Springer
Page : 320 pages
File Size : 47,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018345952

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Invariant Theory and Tableaux by Dennis Stanton Pdf

This volume stems from a workshop held for the Applied Combinatorics program in March 1988. The central idea of the workshop was the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of integers. Many related topics were discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.

Author : William Fulton
Publisher : Cambridge University Press
Page : 276 pages
File Size : 40,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0521567246

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Young Tableaux by William Fulton Pdf

Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

Author : Hélène Barcelo,Gizem Karaali,Rosa Orellana
Publisher : Unknown
Page : 362 pages
File Size : 49,9 Mb
Release : 2019
Category : Combinatorial analysis
ISBN : 3030051420

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Recent Trends in Algebraic Combinatorics by Hélène Barcelo,Gizem Karaali,Rosa Orellana Pdf

This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools.

Author : William Fulton
Publisher : Unknown
Page : 271 pages
File Size : 44,5 Mb
Release : 1997
Category : MATHEMATICS
ISBN : 1107088933

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Young Tableaux by William Fulton Pdf

Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

Author : Shreeram Shankar Abhyankar
Publisher : Unknown
Page : 544 pages
File Size : 54,7 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015014351384

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Enumerative Combinatorics of Young Tableaux by Shreeram Shankar Abhyankar Pdf

Author : Francois Bergeron
Publisher : CRC Press
Page : 227 pages
File Size : 53,6 Mb
Release : 2009-07-06
Category : Mathematics
ISBN : 9781439865071

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Algebraic Combinatorics and Coinvariant Spaces by Francois Bergeron Pdf

Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and

Author : G.M. Piacentini Cattaneo,Elisabetta Strickland
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401134248

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Topics in Computational Algebra by G.M. Piacentini Cattaneo,Elisabetta Strickland Pdf

The main purpose of these lectures is first to briefly survey the fundamental con nection between the representation theory of the symmetric group Sn and the theory of symmetric functions and second to show how combinatorial methods that arise naturally in the theory of symmetric functions lead to efficient algorithms to express various prod ucts of representations of Sn in terms of sums of irreducible representations. That is, there is a basic isometry which maps the center of the group algebra of Sn, Z(Sn), to the space of homogeneous symmetric functions of degree n, An. This basic isometry is known as the Frobenius map, F. The Frobenius map allows us to reduce calculations involving characters of the symmetric group to calculations involving Schur functions. Now there is a very rich and beautiful theory of the combinatorics of symmetric functions that has been developed in recent years. The combinatorics of symmetric functions, then leads to a number of very efficient algorithms for expanding various products of Schur functions into a sum of Schur functions. Such expansions of products of Schur functions correspond via the Frobenius map to decomposing various products of irreducible representations of Sn into their irreducible components. In addition, the Schur functions are also the characters of the irreducible polynomial representations of the general linear group over the complex numbers GLn(C).

Author : Roe Goodman,Nolan R. Wallach
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 41,7 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780387798523

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Symmetry, Representations, and Invariants by Roe Goodman,Nolan R. Wallach Pdf

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Author : Frank D. Grosshans,Gian-Carlo Rota,Joel A. Stein
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 47,5 Mb
Release : 1987-12-31
Category : Mathematics
ISBN : 9780821807194

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Invariant Theory and Superalgebras by Frank D. Grosshans,Gian-Carlo Rota,Joel A. Stein Pdf

This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

Author : Chandrajit L. Bajaj
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226284

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Algebraic Geometry and its Applications by Chandrajit L. Bajaj Pdf

Algebraic Geometry and its Applications will be of interest not only to mathematicians but also to computer scientists working on visualization and related topics. The book is based on 32 invited papers presented at a conference in honor of Shreeram Abhyankar's 60th birthday, which was held in June 1990 at Purdue University and attended by many renowned mathematicians (field medalists), computer scientists and engineers. The keynote paper is by G. Birkhoff; other contributors include such leading names in algebraic geometry as R. Hartshorne, J. Heintz, J.I. Igusa, D. Lazard, D. Mumford, and J.-P. Serre.

Author : William Fulton,Joe Harris
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 46,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0387974954

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Representation Theory by William Fulton,Joe Harris Pdf

Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.

Author : Mourad Ismail,Dennis W. Stanton
Publisher : American Mathematical Soc.
Page : 446 pages
File Size : 50,7 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821811504

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$q$-Series from a Contemporary Perspective by Mourad Ismail,Dennis W. Stanton Pdf

This volume presents the proceedings of the Summer Research Conference on q-series and related topics held at Mount Holyoke College (Hadley, Massachusetts). All of the papers were contributed by participants and offer original research. Articles in the book reflect the diversity of areas that overlap with q-series, as well as the usefulness of q-series across the mathematical sciences. The conference was held in honour of Richard Askey on the occasion of his 65th birthday.

Author : Andrzej Białynicki-Birula
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 41,6 Mb
Release : 1989
Category : Mathematics
ISBN : 0821860151

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Group Actions and Invariant Theory by Andrzej Białynicki-Birula Pdf

This volume contains the proceedings of a conference, sponsored by the Canadian Mathematical Society, on Group Actions and Invariant Theory, held in August, 1988 in Montreal. The conference was the third in a series bringing together researchers from North America and Europe (particularly Poland). The papers collected here will provide an overview of the state of the art of research in this area. The conference was primarily concerned with the geometric side of invariant theory, including explorations of the linearization problem for reductive group actions on affine spaces (with a counterexample given recently by J. Schwarz), spherical and complete symmetric varieties, reductive quotients, automorphisms of affine varieties, and homogeneous vector bundles.