A Course in Combinatorics

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Cambridge University Press, Nov 22, 2001 - Mathematics - 602 pages
6 Reviews
Combinatorics, a subject dealing with ways of arranging and distributing objects, involves ideas from geometry, algebra, and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become an essential tool in many scientific fields. In this second edition the authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as graph theory, extremal problems, designs, colorings, and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.
  

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Call me a RMW groupie but I just luv this book and him <3

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Contents

Graphs
1
Trees
12
Colorings of graphs and Ramseys theorem
24
Turáns theorem and extremal graphs
37
Systems of distinct representatives
43
Dilworths theorem and extremal set theory
53
Flows in networks
61
De Bruijn sequences
71
Projective and combinatorial geometries
303
Gaussian numbers and qanalogues
325
Lattices and Möbius inversion
333
Combinatorial designs and projective geometries
351
Difference sets and automorphisms
369
Difference sets and the group ring
383
Codes and symmetric designs
396
Association schemes
405

Two 01 problems addressing for graphs and a hashcoding scheme
77
The principle of inclusion and exclusion inversion formulae
89
Permanents
98
The Van der Waerden conjecture
110
Elementary counting Stirling numbers
119
Recursions and generating functions
129
Partitions
152
01Matrices
169
Latin squares
182
Hadarnard matrices ReedMuller codes
199
Designs
215
Codes and designs
244
Strongly regular graphs and partial geometries
261
Orthogonal Latin squares
283
More algebraic techniques in graph theory
432
Graph connectivity
451
Planarity and coloring
459
Whitney duality
472
Embeddings of graphs on surfaces
491
Electrical networks and squared squares
507
Pólya theory of counting
522
Baranyais theorem
536
Hints and comments on problems
542
Formal power series
578
Name Index
584
Subject Index
590
Copyright

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About the author (2001)

Van Lint of the Eindhoven University of Technology, The Netherlands

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