TAILIEUCHUNG - Lecture Analytic combinatorics (Part 1) - Chapter 9: Words and maps

Chapter 9: Words and maps covers global properties of words (N-letter strings from an M-letter alphabet), which are well-studied in classical combinatorics (because they model sequences of independent Bernoulli trials) and in classical applied algorithmics (because they model input sequences for hashing algorithms). The chapter also covers random maps (N-letter words from an N-letter alphabet) and discusses relationships with trees and permutations. | ANALYTIC COMBINATORICS PART ONE http 9. Words and Mappings Orientation Second half of class Surveys fundamental combinatorial classes. Considers techniques from analytic combinatorics to study them . Includes applications to the analysis of algorithms. AN INTRODUCTION TO THE Analysis Algorithms SECOND EDITION ROBERT SED GEWICK PHILIPPE FLAJOLET chapter combinatorial classes type of class type of GF 6 Trees unlabeled OGFs 7 Permutations labeled EGFs 8 Strings and Tries unlabeled OGFs 9 Words and Mappings labeled EGFs Note Many more examples in book than in lectures. 2 ANALYTIC COMBINATORICS PART ONE http 9. Words and Mappings Words Birthday problem Coupon collector problem Hash tables Mappings .

• Kỹ thuật lập trình
• Analytic combinatorics
• Lecture Analytic combinatorics
• Combinatorial structures
• Hashing with separate chaining
• Birthday paradox
• Integer factorization
• 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
• 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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