The Best Combinatorics Books 2025

1. Foundations of Combinatorics with Applications [Paperback - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Covers basic counting, functions, decision trees, and sieving methods; fundamental concepts in graph theory and a sampler of graph topics; induction and recursion, sorting theory, and rooted plane trees. Numerous exercises (some with solutions), notes, and references. Includes 75 figures. Appendixes.

Foundations of Combinatorics with Applications, Used [Paperback]

2. On the Foundations of Combinatorial Theory : Combinatorial Geometries, Used [Paperback]

It has been clear within the last ten years that combinatorial geometry, together with its order-theoretic counterpart, the geometric lattice, can serve to catalyze the whole field of combinatorial theory, and a major aim of this book, now available in a preliminary edition, is to present the theory in a form accessible to mathematicians working in disparate subjects. Earlier studies have been one-sided or restricted in their point of view; they were motivated primarily by the desire to extend the classical theory of graphs, or were lattice-theoretic approaches confined to axiomatics and algebraic dependence. These approaches largely ignored the original geometric motivations. The present work brings all these aspects together in order to emphasize the many-sidedness of combinatorial geometry, and to point up the unifying role it may well play in current developments in combinatorics and its applications. The book defines the axiomatics of combinatorial geometry, describes a variety of geometrical examples, and discusses the notion of a strong map between geometries. In addition, there is a brief presentation of coordinatization theory and a sketch of two important lines of future work, the "critical problem" and matching theory. The full chapter titles are given below. Contents:1. Introduction. 2. Geometrics and Geometric Lattices. 3. Six Classical Examples. 4. Span, Bases, Bonds, Dependence, and Circuits. 5. Cryptomorphic Versions of Geometry. 6. Simplicial Geometries. 7. Semimodular Functions. 8. A Glimpse of Matching Theory. 9. Maps. 10. The Extension Theorem. 11. Orthogonality. 12. Factorization of Relatively Complemented Lattices. 13. Factorization of Geometries. 14. Connected Sets. 15. Representation. 16. The Critical Problem. 17. Bibliography.

On the Foundations of Combinatorial Theory : Combinatorial Geometries, Used [Paperback]

3. Combinatorics, Used [Hardcover]

Are you thinking of studying at university in Britain? Do you feel confused about which course is best for you, about which university to choose, about how to apply and are you wondering about what kinds of challenges you will have and how best to overcome them? If so, this guidebook is for you. It will help you to develop the self-understanding and cultural understanding of UK Higher Education and provides the information you need to help you make the right choice about which course and which university to choose and once there what challenges to expect and how best to approach these. It explains how to apply and how to make the best of this lifetime investment both academically and socially once accepted. It explains the opportunities that UK higher education study offers and the pitfalls to avoid. Armed with this guide you will be better prepared culturally and academically to succeed.The guide aims to provide you with a clear understanding of how British universities function, about how best to undertake your studies and how best to enjoy your time there. It aims to address your hopes and to explore your expectations; offering self analytical exercises on how best to realise and adapt these to the new environment. It also addresses your possible concerns and worries about of living and studying in a foreign culture and works to provide you with information and strategies on how best to overcome these.

Combinatorics, Used [Hardcover]

4. Stable Marriage and Its Relation to Other Combinatorial Problems : An Introduction to the Mathematical Analysis of Algorithms, Used [Paperback]

The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms. The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms. Donald E. Knuth was the 1996 recipient of the prestigious Kyoto Prize in the Advanced Technology category for his tremendous contributions to the development of 20th-century computer sciences through both research and education. The Kyoto Prize is Japan's highest private award for lifetime achievement.

Stable Marriage and Its Relation to Other Combinatorial Problems : An Introduction to the Mathematical Analysis of Algorithms, Used [Paperback]

5. Combinatorics and Partially Ordered Sets : Dimension Theory, Used [Hardcover]

Primarily intended for research mathematicians and computer scientists, Combinatorics and Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students in either field. William Trotter concentrates on combinatorial topics for finite partially ordered sets, and with dimension theory serving as a unifying theme, research on partially ordered sets or posets is linked to more traditional topics in combinatorial mathematics -- including graph theory, Ramsey theory, probabilistic methods, hypergraphs, algorithms, and computational geometry. The book's most important contribution is to collect, organize, and explain the many theorems on partially ordered sets in a way that makes them available to the widest possible audience. Chapters: Introduction to Dimension ? Crowns, Splits, Stacks, Sums and Products ? Characterization Problems for Posets, Lattices, Graphs, and Families of Sets ? Hypergraph Coloring, Computational Complexity, and Irreducible Posets ? Planar Posets and Trees ? Planar Graphs, Planar Maps and Convex Polytopes ? Probabilistic Methods in Dimension Theory ? Interval and Geometric Containment Orders ? Greedy Dimension, Back-Tracking, and Depth First Search ? Products of Chains of Bounded Length ? Large Minimal Realizers

Combinatorics and Partially Ordered Sets : Dimension Theory, Used [Hardcover]

6. Polysymmetrics, Used [Paperback]

June Oliver shows how patterns can be built from tiles, which are squares, triangles or hexagons. She shows how to design tiles which are particularly interesting and which fit together to make attractive patterns. Included are twelve full pages of patterns to colour, together with their original tiles, giving a clear demonstration of the possibilities of the technique.

Polysymetrics : The Art of Making Geometric Patterns, Used [Paperback]

7. Combinatorial Algorithms: Theory and Practice [Hardcover - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. Combinatorial Algorithms: Theory and Practice by Edward M. Reingold; Jurg Nievergelt; Narsingh Deo

Combinatorial Algorithms: Theory and Practice, Used [Hardcover]

8. The Stanford GraphBase: A Platform for Combinatorial Computing [Hardcover - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. This book represents the first fruits of Donald E Knuth's preparation for Volume 4 of The Art of Computer Programming. The book's first goal is to demonstrate, through about 30 examples, the art of literate programming. Each example is a programmatic essay, a short story that can be read and enjoyed by humans as readily as it can be read and interpreted by machines. In these essay/progrcms, Knuth makes new contributions to the expositions of several important algorithms and dcta structures, so the programs are of special interest for their content as well as for their style. Tue book's second goal is to provide a concise means for comparing combinatorial algorithms cnd for evaluating methods of combinatorial computing. To this end, Knuth's programs offer standard, freely available sets of dctc - the Standford GraphBose that may be used cs benchmarks to test competing methods.

The Stanford GraphBase : A Platform for Combinatorial Computing, Used [Hardcover]

9. Introduction to Enumerative Combinatorics (Walter Rudin Student Series in Advanced Mathematics) [Hardcover - Used]

CONDITION - USED - Pages can include limited notes and highlighting, and the copy can include "From the library of" labels or previous owner inscriptions. Accessories such as CD, codes, toys, may not be included. Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklos Bona's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course. This text is part of the Walter Rudin Student series in Advanced Mathematics.

Introduction to Enumerative Combinatorics, Used [Hardcover]

10. Applied Combinatorics, Used [Hardcover]

This text presents techniques and applications of combinatorics.

Applied Combinatorics, Used [Hardcover]