Lectures In Algebraic Combinatorics

Author : Adriano M. Garsia,Ömer Eğecioğlu
Publisher : Springer Nature
Page : 243 pages
File Size : 44,6 Mb
Release : 2020-10-06
Category : Mathematics
ISBN : 9783030583736

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Lectures in Algebraic Combinatorics by Adriano M. Garsia,Ömer Eğecioğlu Pdf

Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.

Author : Peter Orlik,Volkmar Welker
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 48,8 Mb
Release : 2007-07-23
Category : Mathematics
ISBN : 9783540683766

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Algebraic Combinatorics by Peter Orlik,Volkmar Welker Pdf

This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions. Both topics are essential parts of current research in a variety of mathematical fields, and the present book makes these sophisticated tools available for graduate students.

Author : Rudolf Ahlswede,Vladimir Blinovsky
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 41,8 Mb
Release : 2008-05-17
Category : Mathematics
ISBN : 9783540786023

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Lectures on Advances in Combinatorics by Rudolf Ahlswede,Vladimir Blinovsky Pdf

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

Author : Alexandru Nica,Roland Speicher
Publisher : Cambridge University Press
Page : 430 pages
File Size : 53,8 Mb
Release : 2006-09-07
Category : Mathematics
ISBN : 9780521858526

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Lectures on the Combinatorics of Free Probability by Alexandru Nica,Roland Speicher Pdf

This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Author : Alla Detinko,Dane Flannery,Eamonn O'Brien
Publisher : Springer
Page : 107 pages
File Size : 54,5 Mb
Release : 2013-01-13
Category : Mathematics
ISBN : 9781447148142

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Probabilistic Group Theory, Combinatorics, and Computing by Alla Detinko,Dane Flannery,Eamonn O'Brien Pdf

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a forum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.

Author : Holger Brenner,Jürgen Herzog,Jurgen Herzog,Orlando E. Villamayor
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 49,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821844342

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Three Lectures on Commutative Algebra by Holger Brenner,Jürgen Herzog,Jurgen Herzog,Orlando E. Villamayor Pdf

This book provides careful and detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications. The book is based on courses at the Winter School on Commutative Algebra and Applications held in Barcelona: Tight closure and vector bundles, by H. Brenner; Combinatorics and commutative algebra, by J. Herzog; and Constructive desingularization, by O. Villamayor. The exposition is aimed at graduate students who have some experience with basic commutative algebra or algebraic geometry but may also serve as an introduction to these modern approaches for mathematicians already familiar with commutative algebra. This book is published in cooperation with Real Sociedad Matematica Espanola.

Author : Chris Godsil
Publisher : Routledge
Page : 329 pages
File Size : 48,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351467506

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Algebraic Combinatorics by Chris Godsil Pdf

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Author : Larry Guth
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 46,6 Mb
Release : 2016-06-10
Category : Combinatorial analysis
ISBN : 9781470428907

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Polynomial Methods in Combinatorics by Larry Guth Pdf

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

Author : M. Lothaire
Publisher : Unknown
Page : 504 pages
File Size : 40,7 Mb
Release : 2002
Category : Combinatorial analysis
ISBN : 1107095875

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Algebraic Combinatorics on Words by M. Lothaire Pdf

Author : Louis J. Billera
Publisher : Unknown
Page : 198 pages
File Size : 48,7 Mb
Release : 1995
Category : Combinatorial analysis
ISBN : 1470439824

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Formal Power Series and Algebraic Combinatorics, 1994 by Louis J. Billera Pdf

This book is devoted to the lectures presented at the Sixth International Conference on Formal Power Series and Algebraic Combinatorics held at DIMACS in May 1994. The conference attracted approximately 180 graduate students and junior and senior researchers from all over the world. Generally speaking, algebraic combinatorics involves the use of techniques from algebra, algebraic topology, and algebraic geometry in solving combinatorial problems; or it involves using combinatorial methods to attack problems in these areas. Combinatorial problems amenable to algebraic methods can arise in these.

Author : K. P. Shum
Publisher : World Scientific
Page : 384 pages
File Size : 47,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812790002

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Advances in Algebra and Combinatorics by K. P. Shum Pdf

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Author : K. P. Shum
Publisher : World Scientific
Page : 384 pages
File Size : 50,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812790019

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Advances in Algebra and Combinatorics - Proceedings of the Second International Congress in Algebra and Combinatorics by K. P. Shum Pdf

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885874

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Topics in Combinatorial Group Theory by Gilbert Baumslag Pdf

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,8 Mb
Release : 2024-06-12
Category : Electronic
ISBN : 9789814472135

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Advances in Algebra and Combinatorics by Anonim Pdf

Author : Sergei K. Lando
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 50,6 Mb
Release : 2003-10-21
Category : Mathematics
ISBN : 9780821834817

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Lectures on Generating Functions by Sergei K. Lando Pdf

In combinatorics, one often considers the process of enumerating objects of a certain nature, which results in a sequence of positive integers. With each such sequence, one can associate a generating function, whose properties tell us a lot about the nature of the objects being enumerated. Nowadays, the language of generating functions is the main language of enumerative combinatorics. This book is based on the course given by the author at the College of Mathematics of the Independent University of Moscow. It starts with definitions, simple properties, and numerous examples of generating functions. It then discusses various topics, such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications of generating functions to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the reader is motivated by interesting examples rather than by general theories. It also contains a lot of exercises to help the reader master the material. Little beyond the standard calculus course is necessary to understand the book. It can serve as a text for a one-semester undergraduate course in combinatorics.