## e-books in Combinatorics category

**Notes on the Combinatorial Fundamentals of Algebra**

by

**Darij Grinberg**-

**arXiv.org**,

**2021**

This is a detailed survey, with rigorous and self-contained proofs, of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants.

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**3098**views)

**Counting Rocks! An Introduction to Combinatorics**

by

**Henry Adams, et al.**-

**arXiv.org**,

**2021**

This textbook is an interactive introduction to combinatorics at the undergraduate level. The major topics in this text are counting problems, proof techniques, recurrence relations and generating functions, and an introduction to graph theory.

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**3443**views)

**An Introduction to Combinatorics and Graph Theory**

by

**David Guichard**-

**Whitman College**,

**2017**

The book covers the classic parts of Combinatorics and graph theory, with some recent progress in the area. Contents: Fundamentals; Inclusion-Exclusion; Generating Functions; Systems of Distinct Representatives; Graph Theory; Polya-Redfield Counting.

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**8217**views)

**Combinatorial Theory**

by

**Gian-Carlo Rota**,

**1998**

In 1998, Gian-Carlo Rota gave his famous course at MIT. John N. Guidi took notes in a verbatim manner conveying the substance of the course. Topics covered included sets, relations, enumeration, order, matching, matroids, and geometric probability.

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**6900**views)

**Enumerative Combinatorics: Volume 1**

by

**Richard P. Stanley**-

**MIT**,

**2011**

The standard guide to the topic for students and experts alike. 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.

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**7084**views)

**Combinatorial Maps: Tutorial**

by

**Dainis Zeps**-

**Latvian University**,

**2007**

Contents: Permutations; Combinatorial maps; The correspondence between combinatorial maps and graphs on surfaces; Map's mirror reflection and dual map; Multiplication of combinatorial maps; Normalized combinatorial maps; Geometrical interpretation...

(

**6927**views)

**Combinatory Analysis**

by

**Percy A. MacMahon**-

**Cambridge University Press**,

**1915**

The object of this work is to present an account of theorems in combinatory analysis which are of a perfectly general character, and to shew the connexion between them by as far as possible bringing them together as parts of a general doctrine ...

(

**7202**views)

**Algebraic and Geometric Methods in Enumerative Combinatorics**

by

**Federico Ardila**-

**arXiv**,

**2014**

The main goal of this survey is to state clearly and concisely some of the most useful tools in algebraic and geometric enumeration, and to give many examples that quickly and concretely illustrate how to put these tools to use.

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**7665**views)

**Foundations of Combinatorics with Applications**

by

**Edward A. Bender, S. Gill Williamson**-

**Dover Publications**,

**2006**

This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.

(

**12025**views)

**Combinatorics Through Guided Discovery**

by

**Kenneth P. Bogart**-

**Dartmouth College**,

**2004**

This is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as 'counting'. The book consists almost entirely of problems.

(

**9871**views)

**Discrepancy Theory**

by

**William Chen**-

**Macquarie University**,

**2012**

Contents: Uniform Distribution; Classical Discrepancy Problem; Generalization of the Problem; Introduction to Lower Bounds; Introduction to Upper Bounds; Fourier Transform Techniques; Upper Bounds in the Classical Problem; Disc Segment Problem; etc.

(

**8234**views)

**Applied Combinatorics**

by

**Mitchel T. Keller, William T. Trotter**-

**Georgia Institute of Technology**,

**2013**

The purpose of the course is to give students a broad exposure to combinatorial mathematics, using applications to emphasize fundamental concepts and techniques. Our approach to the course is to show students the beauty of combinatorics.

(

**9633**views)

**Topics in Algebraic Combinatorics**

by

**Richard P. Stanley**-

**MIT**,

**2013**

Contents: Walks in graphs; Cubes and the Radon transform; Random walks; The Sperner property; Group actions on boolean algebras; Young diagrams and q-binomial coefficients; Enumeration under group action; A glimpse of Young tableaux; etc.

(

**9637**views)

**Notes on Combinatorics**

by

**Peter J. Cameron**-

**Queen Mary, University of London**,

**2007**

Contents: Subsets and binomial coefficients; Selections and arrangements; Power series; Recurrence relations; Partitions and permutations; The Principle of Inclusion and Exclusion; Families of sets; Systems of distinct representatives; etc.

(

**9752**views)

**Matroid Decomposition**

by

**Klaus Truemper**-

**Leibniz**,

**1998**

Matroids were introduced in 1935 as an abstract generalization of graphs and matrices. Matroid decomposition covers the area of the theory dealing with decomposition and composition of matroids. The exposition is clear and simple.

(

**10011**views)

**Combinatorial Geometry with Application to Field Theory**

by

**Linfan Mao**-

**InfoQuest**,

**2009**

Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, etc.

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**15719**views)

**New Perspectives in Algebraic Combinatorics**

by

**Louis J. Billera, at al.**-

**Cambridge University Press**,

**1999**

The rich combinatorial problems arising from the study of various algebraic structures are the subject of the book. It will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.

(

**12255**views)

**Applied Combinatorics**

by

**S. E. Payne**-

**University of Colorado**,

**2003**

These notes deal with enumerative combinatorics. The author included some traditional material and some truly nontrivial material, albeit with a treatment that makes it accessible to the student. He derives a variety of techniques for counting.

(

**16392**views)

**Analytic Combinatorics**

by

**Philippe Flajolet, Robert Sedgewick**-

**Cambridge University Press**,

**2008**

Deals with the the analysis of discrete structures, that emerged over the past years as an essential tool in the understanding of computer programs and models with applications in science. The text contains examples and exercises.

(

**17536**views)

**Combinatorial Algorithms**

by

**Albert Nijenhuis, Herbert S. Wilf**-

**Academic Press Inc**,

**1978**

This is a collection of mathematical algorithms with many new and interesting examples in this second edition. The authors tried to place in the reader's hands a kit of building blocks with which the reader can construct more elaborate structures.

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**19335**views)