A Course in CombinatoricsCombinatorics, 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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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 
542  
Formal power series  578 
Name Index  584 
590  
Common terms and phrases
adjacency matrix algebra automorphism blocks called Chapter circuit codewords coefficients colors combinatorial geometry consider construction contains coordinates Corollary corresponding counting cycle define degree deleting denote the number difference sets digraph edge set eigenvalues elements embedding entries equal equation equivalent exactly Example exists Ferrers diagram finite function graph G Hadamard matrix implies incidence matrix incidence structure induction integers isomorphic lattice Lemma Let G linear Math matrix of order multiplication nset nonnegative nonseparable nonzero number of edges obtained orthogonal Latin squares pairs parameters partial geometry partition path permutation Petersen graph planar planar graph plane of order point set polygon polynomial power series Problem projective plane proof of Theorem prove quadratic form rank sequence Show simple graph spanning trees square of order Steiner system strongly regular graphs subgraph subset subspaces Suppose triangles vector space vertices Whitney duals