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Lectures on Advances in Combinatorics

2008-05-17 Mathematics
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Release : 2008-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 023/5 ( reviews)

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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. This book was released on 2008-05-17. 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 in Geometric Combinatorics

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 402/5 ( reviews)

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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. This book was released on 2006. 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.

Combinatorics Advances

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 54X/5 ( reviews)

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Book Synopsis Combinatorics Advances by : Charles J. Colbourn

Download or read book Combinatorics Advances written by Charles J. Colbourn. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: On March 28~31, 1994 (Farvardin 8~11, 1373 by Iranian calendar), the Twenty fifth Annual Iranian Mathematics Conference (AIMC25) was held at Sharif University of Technology in Tehran, Islamic Republic of Iran. Its sponsors in~ eluded the Iranian Mathematical Society, and the Department of Mathematical Sciences at Sharif University of Technology. Among the keynote speakers were Professor Dr. Andreas Dress and Professor Richard K. Guy. Their plenary lec~ tures on combinatorial themes were complemented by invited and contributed lectures in a Combinatorics Session. This book is a collection of refereed papers, submitted primarily by the participants after the conference. The topics covered are diverse, spanning a wide range of combinatorics and al~ lied areas in discrete mathematics. Perhaps the strength and variety of the pa~ pers here serve as the best indications that combinatorics is advancing quickly, and that the Iranian mathematics community contains very active contributors. We hope that you find the papers mathematically stimulating, and look forward to a long and productive growth of combinatorial mathematics in Iran.

Lessons in Enumerative Combinatorics

2021-05-13 Mathematics
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Release : 2021-05-13
Genre : Mathematics
Kind : eBook
Book Rating : 508/5 ( reviews)

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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. This book was released on 2021-05-13. 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.

Lectures on the Combinatorics of Free Probability

2006-09-07 Mathematics
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Release : 2006-09-07
Genre : Mathematics
Kind : eBook
Book Rating : 526/5 ( reviews)

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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. This book was released on 2006-09-07. 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.

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