An Introduction to the Analysis of Algorithms, Second Edition

Chapter Five. 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. One eventual outgrowth of this observation is that a relatively small set of transfer theorems ultimately yields accurate approximations of the quantities that we seek. Figure 5.1 gives an general overview of the process.

Figure 5.1. An overview of analytic combinatorics