دانلود کتاب Notes for Math 184A (Combinatorics)

فهرست مطالب :

1. Pigeon-hole principle 1.1. Basic version 1.2. General version 2. Induction 2.1. Weak induction 2.2. Strong induction 3. Elementary counting problems 3.1. Functions 3.2. 12-fold way, introduction 3.3. Permutations and combinations 3.4. Words 3.5. Choice problems 4. Partitions and compositions 4.1. Compositions 4.2. Set partitions 4.3. Integer partitions 4.4. 12-fold way, summary 5. Binomial theorem and generalizations 5.1. Binomial theorem 5.2. Multinomial theorem 6. Inclusion-exclusion 7. Formal power series 7.1. Definitions 7.2. Binomial theorem (general form) 8. Ordinary generating functions 8.1. Linear recurrence relations 8.2. Combinatorial interpretations 8.3. Catalan numbers 8.4. Composition of ordinary generating functions 9. Exponential generating functions 9.1. Definitions 9.2. Products of exponential generating functions 9.3. Compositions of exponential generating functions 9.4. Lagrange inversion formula 10. Partially ordered sets 10.1. Definitions and examples 10.2. The incidence algebra 10.3. Möbius inversion