Combinatorics

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.
(3289 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.
(3671 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.
(8461 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.
(7129 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.
(7302 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...
(7195 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 ...
(7451 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.
(7916 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.
(12340 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.
(10111 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.
(8422 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.
(9884 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.
(9805 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.
(9934 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.
(10262 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.
(15959 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.
(12431 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.
(16605 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.
(17795 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.
(19641 views)