Young Tableaux In Combinatorics Invariant Theory And Algebra
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Young Tableaux In Combinatorics Invariant Theory And Algebra
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Author : Joseph P.S. Kung
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Young Tableaux In Combinatorics Invariant Theory And Algebra written by Joseph P.S. Kung and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
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.
Invariant Theory And Tableaux
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Author : Dennis Stanton
language : en
Publisher: Springer
Release Date : 1990
Invariant Theory And Tableaux written by Dennis Stanton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Recent Trends In Algebraic Combinatorics
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Author : Hélène Barcelo
language : en
Publisher: Springer
Release Date : 2019-01-21
Recent Trends In Algebraic Combinatorics written by Hélène Barcelo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
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.
Recent Trends In Algebraic Combinatorics
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Author : Hélène Barcelo
language : en
Publisher:
Release Date : 2019
Recent Trends In Algebraic Combinatorics written by Hélène Barcelo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Combinatorial analysis categories.
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.
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.
Young Tableaux
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Author : William Fulton
language : en
Publisher:
Release Date : 1997
Young Tableaux written by William Fulton and has been published by 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.
Enumerative Combinatorics Of Young Tableaux
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Author : Shreeram Shankar Abhyankar
language : en
Publisher:
Release Date : 1988
Enumerative Combinatorics Of Young Tableaux written by Shreeram Shankar Abhyankar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Symmetry Representations And Invariants
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Author : Roe Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-30
Symmetry Representations And Invariants written by Roe Goodman 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 2009-07-30 with Mathematics categories.
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.
Topics In Computational Algebra
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Author : G.M. Piacentini Cattaneo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In Computational Algebra written by G.M. Piacentini Cattaneo 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.
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).
Algebraic Combinatorics And Coinvariant Spaces
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Author : Francois Bergeron
language : en
Publisher: CRC Press
Release Date : 2009-07-06
Algebraic Combinatorics And Coinvariant Spaces written by Francois Bergeron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Mathematics categories.
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