Chapman and Hall/CRC
232 pages | 30 B/W Illus.
Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand discrete objects. Primarily, the textbook is a gateway to more detailed and involved study and the topics covered such as the interactions between complex analysis and combinatorics will lead readers through number theory, algebraic geometry, probability, and formal language theory.
The textbook starts by discussing objects that can be enumerated using multivariate generating functions, such as permutations, maps, and lattice walks. It also introduces multivariate generating functions and includes a section about the vast topic of the Kernel method, and it discusses diagonals in depth. The second part explains the methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and topology.
A Primer on Combinatorical Calculus
Derived and Transcendental Classes
Generating Functions as Analytic Objects
Singularities of Multvariable Rational Functions
Integration and Multivariable Coefficient Asymptotics