Дискретная математика
Математика
  • формат djvu
  • размер 2.24 МБ
  • добавлен 31 января 2012 г.
Fulton W. Young Tableaux: With Applications to Representation Theory and Geometry
Cambridge University Press, 1997. - 270 Pages.

This book develops the combinatorics of Young tableaux and shows them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of "bumping" and "sliding", and several interesting correspondences. In Part II the author uses these results to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never before appeared in book form. There are numerous exercises throughout, with hints and answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find this book interesting and useful, while students will find the intuitive presentation easy to follow.
Похожие разделы
Смотрите также

Babai L., Frankl P. Linear Algebra Methods in Combinatorics with Applications to Geometry and Computer Science

  • формат djvu
  • размер 2.29 МБ
  • добавлен 04 октября 2011 г.
Dept. of Computer Science, University of Chicago, 1992, -225 pp. Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent years. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint for the plausibility of some link between the two ar...

Berge C. Hypergraphs. Combinatorics of Finite Sets

  • формат pdf
  • размер 10.73 МБ
  • добавлен 04 октября 2011 г.
Издательство North Holland, 1989, -267 pp. For the past forty years, Graph Theory has proved to be an extremely useful tool for solving combinatorial problems, in areas as diverse as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It was thus natural to try and generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint too...

Betten (etc.) Error-Correcting Linear Codes. Classification by Isometry and Applications

  • формат pdf
  • размер 6.67 МБ
  • добавлен 05 декабря 2011 г.
Издательство Springer, 2006, -818 pp. The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. Being an applied discipline by definition, a surprisingly large number of pure mathematical areas tie into Coding Theory. If one were to name just the most important connections, one wo...

Kisacanin B. Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry

  • формат djvu
  • размер 1.31 МБ
  • добавлен 31 января 2012 г.
Kluwer Academic Publishers, 2002. - 220 pages. Key to Symbols. Set Theory. Sets and Elementary Set Operations. Cartesian Product and Relations. Functions and Operations. Cardinality. Problems. Combinatorics. Four Enumeration Principles. Introductory Problems. Basic Definitions. Generating Functions. Problems. Number Theory. Divisibility of Numbers. Important Functions in Number Theory. Congruences. Diophantine Equations. Problems. Geometry. Prope...

Lovasz L. An Algorithmic Theory of Numbers, Graphs, and Convexity

  • формат djvu
  • размер 824.05 КБ
  • добавлен 28 октября 2011 г.
Society for Industrial and Applied Mathematics, 1986, -96 pp. There is little doubt that the present explosion of interest in the algorithmic aspects of mathematics is due to the development of computers — even though special algorithms and their study can be traced back all the way through the history of mathematics. Mathematics started out in Egypt and Babylon as a clearly algorithmic science. In ancient Greece the foundations of its "descript...

Moschovakis Y. Notes on Set Theory

  • формат pdf
  • размер 1.8 МБ
  • добавлен 29 октября 2011 г.
Издательство Springer, 2006, -284 pp. Серия Undergraduate Texts in Mathematics What this book is about. The theory of sets is a vibrant, exciting mathematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foundation of mathematics: it is alleged that all mathematical objects are sets, and...

Rosen K.H., Michaels J.G. et al. Handbook of Discrete and Combinatorial Mathematics

  • формат djvu
  • размер 8.11 МБ
  • добавлен 31 января 2012 г.
Crc press, 2000. - 1183 pages. The Handbook of Discrete and Combinatorial Mathematics is the first book presenting a comprehensive collection of reference material for the essential areas of discrete mathematics as well as for important applications to computer science and engineering. Topics include logic and foundations, counting, number theory, abstract and linear algebra, probability, graph theory, networks and optimization, cryptography and...

Voloshin V.I. Introduction to Graph Theory

  • формат pdf
  • размер 1.46 МБ
  • добавлен 14 ноября 2011 г.
Nova Science Publishers, 2009. - 144 pages. Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of 'computerised' society for which traditional areas of mathematics such as algebra or calculus are powerless. This book is for math and comp...

Wallis W.D. A Beginner's Guide to Discrete Mathematics

  • формат pdf
  • размер 3.56 МБ
  • добавлен 17 ноября 2011 г.
Birkhauser, 2011. - 440 pages. This second edition of A Beginner’s Guide to Discrete Mathematics presents a detailed guide to discrete mathematics and its relationship to other mathematical subjects including set theory, probability, cryptography, graph theory, and number theory. This textbook has a distinctly applied orientation and explores a variety of applications. Key Features of the second edition: * Includes a new chapter on the theory...

Wilf H.S. Generatingfunctionology

  • формат pdf
  • размер 1.54 МБ
  • добавлен 03 июля 2011 г.
A K Peters, 2006. - 245 pages. Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in. * Combinatorics. * Probability Theory. * Statistics. * Theory of Markov Chains. * Number Theory. One of the most important and relevant recent applications of combinatorics lies in th...