Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
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7 of 7 people found the following review helpful:
5.0 out of 5 stars
The Gems of Combinatorics,
This review is from: Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability (Paperback)
This book provides an excellent introduction to a wide variety of extremely active areas of combinatorics. It focuses on the "gems" of the field -- proofs and results which are simultaneously deep, central, and beautiful. One particular feature is the section on infinte Ramsey theory which presents this beautiful but taxing area in an exceptionally clear fashion. There are many good exercises.
6 of 6 people found the following review helpful:
5.0 out of 5 stars
A Classic in Combinatorics,
By Ramanan (Chennai, India.) - See all my reviews
This review is from: Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability (Paperback)
This is the book from which I learnt Combinatorics the Erdosian way. One of the most pleasing qualities of the book is the bite-sized chapters. Perhaps this is one of the first books to start this trend. An earlier reviewer mentions the Ramsey theory chapter which I too would recommend. The chapters on Intersecting hypergraphs, Kruskal-Katona theorem, Littlewood--Offord problem, Four--functions theorem are other gems which come to mind readily. The proofs are crisp and the way the theorems are motivated means that they are not too demanding for a beginning graduate. This is the best and fastest introduction to the way Hungarian Combinatorists operate. An indispensable addition to any aspiring Combinatorist's book shelf.
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Inside This Book
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First Sentence:
All we shall do in this brief section is define the basic concepts and introduce some of the notation we shall need in the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
colex order, infinite monochromatic subset, extremal hypergraph, maximal intersecting family, independent transversal, monotone increasing properties, monotone increasing property, symmetric chains, monochromatic set, trivial necessary condition, intersecting families, extremal graph, covering graph, disjoint edges, distinct representatives, vertex boundary, lower shadow, combinatorial theory, triple system, maximal size, distributive lattice, maximal chains, rank function, set system, threshold function New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
All we shall do in this brief section is define the basic concepts and introduce some of the notation we shall need in the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
colex order, infinite monochromatic subset, extremal hypergraph, maximal intersecting family, independent transversal, monotone increasing properties, monotone increasing property, symmetric chains, monochromatic set, trivial necessary condition, intersecting families, extremal graph, covering graph, disjoint edges, distinct representatives, vertex boundary, lower shadow, combinatorial theory, triple system, maximal size, distributive lattice, maximal chains, rank function, set system, threshold function New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- Ramsey Theory (Wiley-Interscience Series in Discrete Mathematics) by Ronald L. Graham in Back Matter
- Algebraic theory of lattices by Peter Crawley in Back Matter
- Combinatorial Problems and Exercises, Second Edition by L. Lovász in Back Matter
- Combinatorial Theory (Wiley Classics Library) by Marshall Hall in Back Matter
- Ordered Sets (NATO Science Series C: (closed)) by Ivan Rival in Back Matter
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