Analytic Combinatorics

Introduction Analytic Combinatorics uses techniques from complex analysis to find estimates for the coefficients of generating functions. It relates the discrete world of enumerative combinatorics to the continuous world of complex analysis. The term was coined by Philippe Flajolet and Robert Sedgewick, although its techniques can be traced back to at least the early 20th century to the work of Srinivasa Ramanujan and G. H. Hardy. Prerequisites This book assumes you already have a reasonable understanding of generating functions. It assumes little to no understanding of complex analysis. It should explain any complex analysis that you need to know. Chapters Introduction: The shape of different generating functions Asymptotic Analysis Cauchy-Hadamard theorem Meromorphic Functions Meromorphic Functions with Multiple Dominant Singularities Tauberian Theorem Cauchy's coefficient formula and Cauchy's inequality Meromorphic Functions using the Residue Method Darboux Method Singularity Analysis Saddle-point Method Discrete mathematics Mathematical analysis University level mathematics books 75%