Enumerative Combinatorics

Enumerative Combinatorics  PDF Book Detail:
Author: Richard P. Stanley
Publisher: Cambridge University Press
ISBN: 9781107602625
Size: 28.68 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 642
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Book Description: 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 material in Volume 1 was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods, partially ordered sets, and rational generating functions. Much of the material is related to generating functions, a fundamental tool in enumerative combinatorics. In this new edition, 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.

Enumerative Combinatorics

Enumerative Combinatorics  PDF Book Detail:
Author: Richard P. Stanley
Publisher: Cambridge University Press
ISBN: 1139810995
Size: 53.90 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages :
View: 5699

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Book Description: This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, 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 on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

Enumerative Combinatorics Volume 1

Enumerative Combinatorics  Volume 1 PDF Book Detail:
Author: Richard P. Stanley
Publisher: Cambridge University Press
ISBN: 9780521663519
Size: 44.16 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 340
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Book Description: An introduction, suitable for graduate students, showing connections to other areas of mathematics.

Lehrbuch Der Combinatorik

Lehrbuch der Combinatorik PDF Book Detail:
Author: Eugen Netto
Publisher:
ISBN:
Size: 10.34 MB
Format: PDF, ePub, Mobi
Category : Combinations
Languages : de
Pages : 260
View: 1461

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Book Description:

Counting The Art Of Enumerative Combinatorics

Counting  The Art of Enumerative Combinatorics PDF Book Detail:
Author: George E. Martin
Publisher: Springer Science & Business Media
ISBN: 1475748787
Size: 28.22 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 252
View: 1244

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Book Description: This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Catalan Numbers

Catalan Numbers PDF Book Detail:
Author: Richard P. Stanley
Publisher: Cambridge University Press
ISBN: 1316299589
Size: 30.63 MB
Format: PDF
Category : Mathematics
Languages : en
Pages :
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Book Description: Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here.

Das Buch Der Beweise

Das BUCH der Beweise PDF Book Detail:
Author: Martin Aigner
Publisher: Springer-Verlag
ISBN: 3662064545
Size: 80.68 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : de
Pages : 247
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Book Description: Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

Vorlesungen Ber Differenzenrechnung

Vorlesungen   ber Differenzenrechnung PDF Book Detail:
Author: Niels Erik Nörlund
Publisher: Springer-Verlag
ISBN: 3642508243
Size: 30.39 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : de
Pages : 554
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Book Description: Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Diskrete Mathematik

Diskrete Mathematik PDF Book Detail:
Author: Anusch Taraz
Publisher: Springer-Verlag
ISBN: 376438901X
Size: 33.60 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : de
Pages : 137
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Book Description: Dieses Buch führt kompakt in einige Kerngebiete der Diskreten Mathematik ein. Es behandelt grundlegende Konzepte der Kombinatorik und Graphentheorie und konzentriert sich auf thematische Einheiten wie endliche Geometrien und Ramseytheorie sowie auf methodische Schwerpunkte wie probabilistische und algebraische Techniken. Die Diskrete Mathematik zeigt sich hier als eine spannende Disziplin mit Fragestellungen, die zahlreiche Bezüge zu klassischen Anfängervorlesungen hat. Das Buch ist für zwei- bis vierstündige Lehrveranstaltungen geeignet.

Permutation Patterns

Permutation Patterns PDF Book Detail:
Author: Steve Linton
Publisher: Cambridge University Press
ISBN: 1139488848
Size: 56.70 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages :
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Book Description: The study of permutation patterns is a thriving area of combinatorics that relates to many other areas of mathematics, including graph theory, enumerative combinatorics, model theory, the theory of automata and languages, and bioinformatics. Arising from the Fifth International Conference on Permutation Patterns, held in St Andrews in June 2007, this volume contains a mixture of survey and research articles by leading experts, and includes the two invited speakers, Martin Klazar and Mike Atkinson. Together, the collected articles cover all the significant strands of current research: structural methods and simple patterns, generalisations of patterns, various enumerative aspects, machines and networks, packing, and more. Specialists in this area and other researchers in combinatorics and related fields will find much of interest in this book. In addition, the volume provides plenty of material accessible to advanced undergraduates and is a suitable reference for projects and dissertations.