Principles and Techniques in Combinatorics
Search in google:
PrefaceNotation and AbbreviationContents1Permutations and Combinations11.1Two Basic Counting Principles11.2Permutations61.3Circular Permutations121.4Combinations171.5The Injection and Bijection Principles271.6Arrangements and Selections with Repetitions321.7Distribution Problems402Binomial Coefficients and Multinomial Coefficients692.2The Binomial Theorem702.3Combinatorial Identities712.4The Pascal's Triangle762.5Chu Shih-Chieh's Identity782.6Shortest Routes in a Rectangular Grid852.7Some Properties of Binomial Coefficients932.8Multinomial Coefficients and the Multinomial Theorem963The Pigeonhole Principle and Ramsey Numbers1193.2The Pigeonhole Principle1193.3More Examples1223.4Ramsey Type Problems and Ramsey Numbers1293.5Bounds for Ramsey Numbers1324The Principle of Inclusion and Exclusion1454.2The Principle1464.3A Generalization1484.4Integer Solutions and Shortest Routes1534.5Surjective Mappings and Stirling Numbers of the Second Kind1584.6Derangements and A Generalization1604.7The Sieve of Eratosthenes and Euler [phi]-function1634.8The 'Probleme des Menages'1695Generating Functions1855.1Ordinary Generating Functions1855.2Some Modelling Problems1925.3Partitions of Integers1965.4Exponential Generating Functions2046Recurrence Relations2256.2Two Examples2286.3Linear Homogeneous Recurrence Relations2346.4General Linear Recurrence Relations2416.5Two Applications2446.6A System of Linear Recurrence Relations2516.7The Method of Generating Functions2566.8A Nonlinear Recurrence Relation and Catalan Numbers2596.9Oscillating Permutations and an Exponential Generating Function262Bibliography287Answers289Index297
