TAILIEUCHUNG - Lecture Analytic combinatorics (Part 1) - Chapter 5: Analytic combinatorics

This chapter introduces analytic combinatorics, a modern approach to the study of combinatorial structures of the sort that we encounter frequently in the analysis of algorithms. The approach is predicated on the idea that combinatorial structures are typically defined by simple formal rules that are the key to learning their properties. | ANALYTIC COMBINATORICS PART ONE http 5. Analytic Combinatorics Analytic combinatorics is a calculus for the quantitative study of large combinatorial structures. Features Analysis begins with formal combinatorial constructions. The generating function is the central object of study. Transfer theorems can immediately provide results from formal descriptions. Results extend in principle to any desired precision on the standard scale. Variations on fundamental constructions are easily handled. combinatorial symbolic generating function equation analytic coefficient constructions transfer theorem transfer theorem asymptotics the symbolic method 2 Analytic combinatorics is a calculus for the quantitative study of large combinatorial structures. Ex How many binary trees with N nodes T E Z X T X T 7 z 1 zT z 2 4n N combinatorial construction GF equation coefficient asymptotics

• Kỹ thuật lập trình
• Analytic combinatorics
• Lecture Analytic combinatorics
• Combinatorial structures
• Unlabelled classes
• Labelled classes
• Symbolic method for parameters
• Compare algorithms
• Analysis of algorithms
• Scientific approach
• Computing values
• Types of recurrences
• Master theorem
• Ordinary generating functions
• Exponential generating functions
• Generating functions
• Asymptotic approximation
• Asymptotic expansions
• Manipulating asymptotic expansions
• Binary trees
• Combinatorial equivalences
• Properties of trees
• Algorithms on permutations
• Representations of permutations
• Situ permutation
• String searching
• Combinatorial properties of bitstrings
• Trie algorithms
• Hashing with separate chaining
• Birthday paradox
• Integer factorization
• Symbolic method
• Combinatorial class
• Labelled structures
• Labelled trees
• Combinatorial parameters
• Moment calculations
• Complex analysis
• Meromorphic asymptotics
• Complex functions
• Supercritical sequence schema
• Singularity analysis
• Standard function scale
• Transfer theorems
• Applications of singularity analysis
• Simple varieties of trees
• Saddle point asymptotics
• Modulus surfaces
• Saddle point bounds
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