Название: Analytic Combinatorics: A Multidimensional Approach (Discrete Mathematics and Its Applications) Автор: Marni Mishna
Издательство: Chapman and Hall/CRC
Год: 2020
Формат: true pdf/epub/azw3
Страниц: 252
Размер: 10.8 Mb
Язык: English
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 the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory.
The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry.
Features
Written with combinatorics-centric exposition to illustrate advanced analytic techniques
Each chapter includes problems, exercises, and reviews of the material discussed in them
Includes a comprehensive glossary, as well as lists of figures and symbols