Analytic combinatorics
The idea of analytic combinatorics is to solve the discrete problems through the analysis of the generating functions. Generating functions can be treated both as algebraic objects (formal series ring) and continuous functions. This will lead to many special and interesting techniques.
The course is composed by three parts, 1 the introduction of generatingfunctionology, 2 the symbolic method in enumerative combinatorics, 3 the kernel method.
The course is composed by three parts, 1 the introduction of generatingfunctionology, 2 the symbolic method in enumerative combinatorics, 3 the kernel method.
Lecturer
Date
18th September ~ 18th December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Friday | 13:30 - 16:55 | Shuimo | Tencent A | 482 969 7386 | 106457 |
Prerequisite
complex analysis, calculus, undergraduate algebra
Syllabus
1 calculations of generating functions.
2 snake oil methods, Sieve methods.
3 Symbolic methods of unlabelled and labelled class.
4 the kernel method and basic analytic combinatorics of direct lattice path.
5 graph enumeration, graph coloring.
6 polynomial equation with one catalytic variable.
2 snake oil methods, Sieve methods.
3 Symbolic methods of unlabelled and labelled class.
4 the kernel method and basic analytic combinatorics of direct lattice path.
5 graph enumeration, graph coloring.
6 polynomial equation with one catalytic variable.
Reference
Wilf, Herbert S. generatingfunctionology. CRC press, 2005.
Flajolet, Philippe, and Robert Sedgewick. Analytic combinatorics. cambridge University press, 2009.
Bousquet-Mélou, Mireille, and Arnaud Jehanne. "Polynomial equations with one catalytic variable, algebraic series and map enumeration." Journal of Combinatorial Theory, Series B 96.5 (2006): 623-672.
Banderier, Cyril, and Philippe Flajolet. "Basic analytic combinatorics of directed lattice paths." Theoretical Computer Science 281.1-2 (2002): 37-80.
Bernardi, Olivier, and Mireille Bousquet-Mélou. "Counting colored planar maps: algebraicity results." Journal of Combinatorial Theory, Series B 101.5 (2011): 315-377.
Melczer, Stephen. An Invitation to Analytic Combinatorics. Springer, 2021.
Flajolet, Philippe, and Robert Sedgewick. Analytic combinatorics. cambridge University press, 2009.
Bousquet-Mélou, Mireille, and Arnaud Jehanne. "Polynomial equations with one catalytic variable, algebraic series and map enumeration." Journal of Combinatorial Theory, Series B 96.5 (2006): 623-672.
Banderier, Cyril, and Philippe Flajolet. "Basic analytic combinatorics of directed lattice paths." Theoretical Computer Science 281.1-2 (2002): 37-80.
Bernardi, Olivier, and Mireille Bousquet-Mélou. "Counting colored planar maps: algebraicity results." Journal of Combinatorial Theory, Series B 101.5 (2011): 315-377.
Melczer, Stephen. An Invitation to Analytic Combinatorics. Springer, 2021.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English