Lectures In Algebraic Combinatorics

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Lectures in Algebraic Combinatorics

Author : Adriano M. Garsia
Publisher : Springer Nature
ISBN 13 : 3030583732
Total Pages : 243 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Lectures in Algebraic Combinatorics by : Adriano M. Garsia

Download or read book Lectures in Algebraic Combinatorics written by Adriano M. Garsia and published by Springer Nature. This book was released on 2020-10-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures in Geometric Combinatorics

Author : Rekha R. Thomas
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841402
Total Pages : 156 pages
Book Rating : 4.8/5 (414 download)

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Book Synopsis Lectures in Geometric Combinatorics by : Rekha R. Thomas

Download or read book Lectures in Geometric Combinatorics written by Rekha R. Thomas and published by American Mathematical Soc.. This book was released on 2006 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Algebraic Combinatorics

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
ISBN 13 : 1461469988
Total Pages : 226 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Algebraic Combinatorics by : Richard P. Stanley

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.

A Course in Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis A Course in Combinatorics by : J. H. van Lint

Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Algebraic Combinatorics

Author : Peter Orlik
Publisher : Springer Science & Business Media
ISBN 13 : 3540683763
Total Pages : 182 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Algebraic Combinatorics by : Peter Orlik

Download or read book Algebraic Combinatorics written by Peter Orlik and published by Springer Science & Business Media. This book was released on 2007-07-23 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lessons in Enumerative Combinatorics

Author : Ömer Eğecioğlu
Publisher : Springer Nature
ISBN 13 : 3030712508
Total Pages : 479 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Lessons in Enumerative Combinatorics by : Ömer Eğecioğlu

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.

Algebraic Combinatorics and Computer Science

Author : H. Crapo
Publisher : Springer Science & Business Media
ISBN 13 : 8847021073
Total Pages : 542 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Algebraic Combinatorics and Computer Science by : H. Crapo

Download or read book Algebraic Combinatorics and Computer Science written by H. Crapo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Lectures on Advances in Combinatorics

Author : Rudolf Ahlswede
Publisher : Springer Science & Business Media
ISBN 13 : 3540786023
Total Pages : 318 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Lectures on Advances in Combinatorics by : Rudolf Ahlswede

Download or read book Lectures on Advances in Combinatorics written by Rudolf Ahlswede and published by Springer Science & Business Media. This book was released on 2008-05-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].

Lectures On Algebraic Topology

Author : Haynes R Miller
Publisher : World Scientific
ISBN 13 : 9811231265
Total Pages : 405 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Lectures On Algebraic Topology by : Haynes R Miller

Download or read book Lectures On Algebraic Topology written by Haynes R Miller and published by World Scientific. This book was released on 2021-09-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.

Algebraic Combinatorics I

Author : Eiichi Bannai
Publisher : Addison-Wesley Longman
ISBN 13 :
Total Pages : 464 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Algebraic Combinatorics I by : Eiichi Bannai

Download or read book Algebraic Combinatorics I written by Eiichi Bannai and published by Addison-Wesley Longman. This book was released on 1984-01-21 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on the Combinatorics of Free Probability

Author : Alexandru Nica
Publisher : Cambridge University Press
ISBN 13 : 0521858526
Total Pages : 430 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Lectures on the Combinatorics of Free Probability by : Alexandru Nica

Download or read book Lectures on the Combinatorics of Free Probability written by Alexandru Nica and published by Cambridge University Press. This book was released on 2006-09-07 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Connections Between Algebra, Combinatorics, and Geometry

Author : Susan M. Cooper
Publisher : Springer
ISBN 13 : 1493906267
Total Pages : 328 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Connections Between Algebra, Combinatorics, and Geometry by : Susan M. Cooper

Download or read book Connections Between Algebra, Combinatorics, and Geometry written by Susan M. Cooper and published by Springer. This book was released on 2014-05-16 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Lectures on Algebraic Quantum Groups

Author : Ken Brown
Publisher : Birkhäuser
ISBN 13 : 303488205X
Total Pages : 339 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Lectures on Algebraic Quantum Groups by : Ken Brown

Download or read book Lectures on Algebraic Quantum Groups written by Ken Brown and published by Birkhäuser. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Three Lectures on Commutative Algebra

Author : Holger Brenner
Publisher : American Mathematical Soc.
ISBN 13 : 0821844342
Total Pages : 190 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Three Lectures on Commutative Algebra by : Holger Brenner

Download or read book Three Lectures on Commutative Algebra written by Holger Brenner and published by American Mathematical Soc.. This book was released on 2008 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Combinatorics

Author : Ezra Miller
Publisher : American Mathematical Soc.
ISBN 13 : 0821837362
Total Pages : 705 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Combinatorics by : Ezra Miller

Download or read book Geometric Combinatorics written by Ezra Miller and published by American Mathematical Soc.. This book was released on 2007 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Combinatorial Commutative Algebra

Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 9780387237077
Total Pages : 442 pages
Book Rating : 4.2/5 (37 download)

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Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller

Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Extremal Combinatorics

Author : Stasys Jukna
Publisher : Springer Science & Business Media
ISBN 13 : 3662046504
Total Pages : 389 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Extremal Combinatorics by : Stasys Jukna

Download or read book Extremal Combinatorics written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.