Hjem

Introduction Some Combinatorial Examples Sets, Relations and Proof Techniques Two Principles of Enumeration Graphs Systems of Distinct Representatives Fundamentals of Enumeration Permutations and Combinations Applications of P(n, k) and (n k) Permutations and Combinations of Multisets Applications and Subtle Errors Algorithms Probability Introduction Some Definitions and Easy Examples Events and Probabilities Three Interesting Examples Probability Models Bernoulli Trials The Probabilities in Poker The Wild Card Poker Paradox The Pigeonhole Principle and Ramsey's Theorem The Pigeonhole Principle Applications of the Pigeonhole Principle Ramsey's Theorem -- the Graphical Case Ramsey Multiplicity Sum-Free Sets Bounds on Ramsey Numbers The General Form of Ramsey's Theorem The Principle of Inclusion and Exclusion Unions of Events The Principle Combinations with Limited Repetitions Derangements Generating Functions and Recurrence Relations Generating Functions Recurrence Relations From Generating Function to Recurrence Exponential Generating Functions Catalan, Bell and Stirling Numbers Introduction Catalan Numbers Stirling Numbers of the Second Kind Bell Numbers Stirling Numbers of the First Kind Computer Algebra and Other Electronic Systems Symmetries and the P´olya-Redfield Method Introduction Basics of Groups Permutations and Colorings An Important Counting Theorem P´olya and Redfield's Theorem Partially-Ordered Sets Introduction Examples and Definitions Bounds and lattices Isomorphism and Cartesian products Extremal set theory: Sperner's and Dilworth's theorems Introduction to Graph Theory Degrees Paths and Cycles in Graphs Maps and Graph Coloring Further Graph Theory Euler Walks and Circuits Application of Euler Circuits to Mazes Hamilton Cycles Trees Spanning Trees Coding Theory Errors; Noise The Venn Diagram Code Binary Codes; Weight; Distance Linear Codes Hamming Codes Codes and the Hat Problem Variable-Length Codes and Data Compression Latin Squares Introduction Orthogonality Idempotent Latin Squares Partial Latin Squares and Subsquares Applications Balanced Incomplete Block Designs Design Parameters Fisher's Inequality Symmetric Balanced Incomplete Block Designs New Designs from Old Difference Methods Linear Algebra Methods in Combinatorics Recurrences Revisited State Graphs and the Transfer Matrix Method Kasteleyn's Permanent Method Appendix
1: Sets; Proof Techniques7 Appendix
2: Matrices and Vectors Appendix
3: Some Combinatorial People