Permutation Enumeration of the Symmetric Group and the Combinatorics of Symmetric Functions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Permutation Enumeration of the Symmetric Group and the Combinatorics of Symmetric Functions PDF full book. Access full book title Permutation Enumeration of the Symmetric Group and the Combinatorics of Symmetric Functions by Desiree A. Beck. Download full books in PDF and EPUB format.
Author: Desiree A. Beck
Publisher:
ISBN:
Category :
Languages : en
Pages : 80
Get Book Here
Book Description
Author: Desiree A. Beck
Publisher:
ISBN:
Category :
Languages : en
Pages : 80
Get Book Here
Book Description
Author: Desiree Anne Beck
Publisher:
ISBN:
Category :
Languages : en
Pages : 402
Get Book Here
Book Description
Author: Jeffrey Remmel
Publisher: Birkhäuser
ISBN: 3319236180
Category : Mathematics
Languages : en
Pages : 297
Get Book Here
Book Description
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: 9780821821541
Category : Computers
Languages : en
Pages : 180
Get Book Here
Book Description
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: Bruce E. Sagan
Publisher: Springer Science & Business Media
ISBN: 1475768044
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
Author: Yan Zhuang
Publisher:
ISBN:
Category : Noncommutative function spaces
Languages : en
Pages : 137
Get Book Here
Book Description
This Ph.D. dissertation is a compilation of material from four papers that develop and apply methods involving noncommutative symmetric functions to permutation enumeration, and in particular to the theory of descent statistics: permutation statistics that depend only on the descent set and length of a permutation. We prove a generalization of Gessel's run theorem and use it to enumerate permutations with parity restrictions on peaks and valleys, and to give a general method for enumerating permutations by descent statistics that are expressible in terms of run lengths. Next, we prove new identities that express Eulerian polynomials in terms of polynomials encoding the distribution of other descent statistics (and vice versa)—including refinements of formulas previously found by Stembridge and Petersen—and enumerate permutations by various descent statistics together with the inversion number. Finally, we introduce the notion of a shuffle-compatible permutation statistic and develop a theory of shuffle-compatibility for descent statistics, unifying previous results of Stanley, Gessel, Stembridge, Aguiar–Bergeron–Nyman, and Petersen.
Author: Daniel Krob
Publisher: Springer Science & Business Media
ISBN: 3662041669
Category : Mathematics
Languages : en
Pages : 815
Get Book Here
Book Description
This book contains the extended abstracts presented at the 12th International Conference on Power Series and Algebraic Combinatorics (FPSAC '00) that took place at Moscow State University, June 26-30, 2000. These proceedings cover the most recent trends in algebraic and bijective combinatorics, including classical combinatorics, combinatorial computer algebra, combinatorial identities, combinatorics of classical groups, Lie algebra and quantum groups, enumeration, symmetric functions, young tableaux etc...
Author: Alain Lascoux
Publisher: American Mathematical Soc.
ISBN: 0821828711
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
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: Jennifer D. Wagner
Publisher:
ISBN:
Category :
Languages : en
Pages : 366
Get Book Here
Book Description
Author: Miklos Bona
Publisher: CRC Press
ISBN: 1135437106
Category : Mathematics
Languages : en
Pages : 400
Get Book Here
Book Description
WINNER of a CHOICE Outstanding Academic Title Award for 2006! As linear orders, as elements of the symmetric group, modeled by matrices, modeled by graphs...permutations are omnipresent in modern combinatorics. They are omnipresent but also multifaceted, and while several excellent books explore particular aspects of the subject, no one book has covered them all. Even the classic results are scattered in various resources. Combinatorics of Permutations offers the first comprehensive, up to date treatment of both enumerative and extremal combinatorics and looks at permutation as linear orders and as elements of the symmetric group. The author devotes two full chapters to the young but active area of pattern avoidance. He explores the quest for the Stanley-Wilf conjecture and includes the recent and spectacular Marcus-Tardos proof of this problem. He examines random permutations and Standard Young Tableaux and provides an overview of the very rich algebraic combinatorics of permutations. The final chapter takes an in-depth look at combinatorial sorting algorithms. The author's style is relaxed, entertaining, and clearly reflects his enthusiasm for the "serious fun" the subject holds. Filled with applications from a variety of fields and exercises that draw upon recent research results, this book serves equally well as a graduate-level text and a reference for combinatorics researchers.
