Permutation Enumeration Of The Symmetric Group And The Combinatorics Of Symmetric Functions

Author : Desiree A. Beck
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.85/5 ( download)

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Download or read book Permutation Enumeration of the Symmetric Group and the Combinatorics of Symmetric Functions written by Desiree A. Beck and published by . This book was released on 1993 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jeffrey Remmel
Publisher : Birkhäuser
ISBN 13 : 3319236180
Total Pages : 292 pages
Book Rating : 4.86/5 ( download)

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Download or read book Counting with Symmetric Functions written by Jeffrey Remmel and published by Birkhäuser. This book was released on 2015-11-28 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Laurent Manivel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821541
Total Pages : 180 pages
Book Rating : 4.47/5 ( download)

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Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.

Author : Desiree Anne Beck
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.64/5 ( download)

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Download or read book Permutation Enumeration of the Symmetric Group and the Hyperoctahedral Group and the Combinatorics of Symmetric Functions written by Desiree Anne Beck and published by . This book was released on 1993 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jeffrey Remmel
Publisher :
ISBN 13 : 9783319236193
Total Pages : pages
Book Rating : 4.99/5 ( download)

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Download or read book Counting with Symmetric Functions written by Jeffrey Remmel and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Anthony Mendes
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.81/5 ( download)

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Download or read book Building Generating Functions Brick by Brick written by Anthony Mendes and published by . This book was released on 2004 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 1439848866
Total Pages : 600 pages
Book Rating : 4.69/5 ( download)

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Download or read book Bijective Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2011-02-10 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical

Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262491
Total Pages : 801 pages
Book Rating : 4.91/5 ( download)

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Download or read book Enumerative Combinatorics written by Richard Stanley and published by Cambridge University Press. This book was released on 2023-08-17 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised second volume of the standard guide to enumerative combinatorics, including the theory of symmetric functions and 159 new exercises.

Author : Steve Linton
Publisher : Cambridge University Press
ISBN 13 : 1139488848
Total Pages : 353 pages
Book Rating : 4.46/5 ( download)

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Download or read book Permutation Patterns written by Steve Linton and published by Cambridge University Press. This book was released on 2010-06-03 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mixture of survey and research articles by leading experts that will be of interest to specialists in permutation patterns and other researchers in combinatorics and related fields. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.

Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262513
Total Pages : 802 pages
Book Rating : 4.14/5 ( download)

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Download or read book Enumerative Combinatorics: Volume 2 written by Richard Stanley and published by Cambridge University Press. This book was released on 2023-07-31 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.