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Author : Shreeram Shankar Abhyankar
Publisher :
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)
Download or read book Enumerative Combinatorics of Young Tableaux written by Shreeram Shankar Abhyankar and published by . This book was released on 1988 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shreeram Shankar Abhyankar
Publisher :
ISBN 13 : 9780598038845
Total Pages : 535 pages
Book Rating : 4.0/5 (388 download)
Download or read book Enumerative Combinatorics of Young Tableaux written by Shreeram Shankar Abhyankar and published by . This book was released on with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William Fulton
Publisher : Cambridge University Press
ISBN 13 : 9780521567244
Total Pages : 276 pages
Book Rating : 4.5/5 (672 download)
Download or read book Young Tableaux written by William Fulton and published by Cambridge University Press. This book was released on 1997 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.
Author : Joseph P.S. Kung
Publisher : Elsevier
ISBN 13 : 1483272028
Total Pages : 344 pages
Book Rating : 4.4/5 (832 download)
Download or read book Young Tableaux in Combinatorics, Invariant Theory, and Algebra written by Joseph P.S. Kung and published by Elsevier. This book was released on 2014-05-12 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Richard P. Stanley
Publisher : Springer Science & Business Media
ISBN 13 : 1461469988
Total Pages : 226 pages
Book Rating : 4.4/5 (614 download)
Download or read book Algebraic Combinatorics written by Richard P. Stanley and published by Springer Science & Business Media. This book was released on 2013-06-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
Author : Richard P. Stanley
Publisher : Cambridge University Press
ISBN 13 : 1107015421
Total Pages : 641 pages
Book Rating : 4.1/5 (7 download)
Download or read book Enumerative Combinatorics: Volume 1 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 2012 with total page 641 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 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.
Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1482220865
Total Pages : 1073 pages
Book Rating : 4.4/5 (822 download)
Download or read book Handbook of Enumerative Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-03-24 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
Author : William Fulton
Publisher :
ISBN 13 : 9781107088931
Total Pages : 271 pages
Book Rating : 4.0/5 (889 download)
Download or read book Young Tableaux written by William Fulton and published by . This book was released on 1997 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.
Author : Susumu Ariki
Publisher : American Mathematical Soc.
ISBN 13 : 0821832328
Total Pages : 169 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representations of Quantum Algebras and Combinatorics of Young Tableaux written by Susumu Ariki and published by American Mathematical Soc.. This book was released on 2002 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Author : Richard P. Stanley
Publisher : Cambridge University Press
ISBN 13 : 9780521789875
Total Pages : 600 pages
Book Rating : 4.7/5 (898 download)
Download or read book Enumerative Combinatorics: Volume 2 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 1997 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.
Author : Hélène Barcelo
Publisher : Springer
ISBN 13 : 3030051412
Total Pages : 362 pages
Book Rating : 4.0/5 (3 download)
Download or read book Recent Trends in Algebraic Combinatorics written by Hélène Barcelo and published by Springer. This book was released on 2019-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ömer Eğecioğlu
Publisher : Springer Nature
ISBN 13 : 3030712508
Total Pages : 479 pages
Book Rating : 4.0/5 (37 download)
Download or read book Lessons in Enumerative Combinatorics written by Ömer Eğecioğlu and published by Springer Nature. This book was released on 2021-05-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.
Author : Bruce E. Sagan
Publisher : Springer Science & Business Media
ISBN 13 : 1475768044
Total Pages : 254 pages
Book Rating : 4.4/5 (757 download)
Download or read book The Symmetric Group written by Bruce E. Sagan and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)
Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
Author : Richard Stanley
Publisher : Cambridge University Press
ISBN 13 : 1009262491
Total Pages : 801 pages
Book Rating : 4.0/5 (92 download)
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 : Andrzej Białynicki-Birula
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860151
Total Pages : 244 pages
Book Rating : 4.8/5 (61 download)
Download or read book Group Actions and Invariant Theory written by Andrzej Białynicki-Birula and published by American Mathematical Soc.. This book was released on 1989 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461241405
Total Pages : 576 pages
Book Rating : 4.4/5 (612 download)
Download or read book Advances in Combinatorial Methods and Applications to Probability and Statistics written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
