Analytic Combinatorics in Several Variables

Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.

離散結構模擬了從DNA序列到互聯網網絡等各種對象。生成函數理論提供了一個代數框架，用於使用數學工具對離散結構進行枚舉。本書是25年來開發分析機械從生成函數中恢復多變量序列的漸近行為的結果，使用多變量方法依賴於分析、代數和拓撲工具的結合。由此產生的多變量解析組合學理論在數學、組合學、計算機科學和自然科學等各個領域中得到應用。這個新版本對研究生學生更加易於理解，增加了許多練習題、使用Sage工作表的計算示例來說明主要結果、更新的背景材料、額外的插圖，以及提供概念概述的新章節。