Analytic combinatorics

History

One of the earliest uses of analytic techniques for an enumeration problem came from Srinivasa Ramanujan and G. H. Hardy's work on integer partitions.

Hayman

Flajolet and Odlyzko

Flajolet and Sedgewick

References

• Melczer, Stephen (2021). An Invitation to Analytic Combinatorics: From One to Several Variables (PDF). Springer Texts & Monographs in Symbolic Computation.
• Pemantle, Robin; Wilson, Mark C. (2013). Analytic Combinatorics in Several Variables (PDF). Cambridge University Press.

Further reading

• De Bruijn, N.G. (1981). Asymptotic Methods in Analysis. Dover Publications.
• Flajolet, Philippe; Odlyzko, Andrew (1990). "Singularity analysis of generating functions" (PDF). SIAM Journal on Discrete Mathematics. 1990 (3).
• Flajolet, Philippe; Sedgewick, Robert (2009). Analytic Combinatorics (PDF). Cambridge University Press.
• Melczer, Stephen (2021). An Invitation to Analytic Combinatorics: From One to Several Variables (PDF). Springer Texts & Monographs in Symbolic Computation.
• Pemantle, Robin; Wilson, Mark C. (2013). Analytic Combinatorics in Several Variables (PDF). Cambridge University Press.
• Szegő, Gabor (1975). Orthogonal Polynomials (4th ed.). American Mathematical Society.
• Wilf, Herbert S. (2006). Generatingfunctionology (PDF) (3rd ed.). A K Peters, Ltd.

External links

• Analytic Combinatorics online course
• An Introduction to the Analysis of Algorithms online course
• Analytic Combinatorics in Several Variables projects
• An Invitation to Analytic Combinatorics
• Philippe Flajolet's Home Page
• Andrew Odlyzko's Home Page