# Publications in the Project

On this page we list the core papers which developed the area of ACSV as it is known today. Readers wanting pedagogical sources developing the theory of ACSV can consult

• An Invitation to Analytic Combinatorics: From One to Several Variables by Stephen Melczer. Texts & Monographs in Symbolic Computation, Springer International Publishing, 2021. (Introduction to the theory aimed at graduate students and those looking to enter the field. There is a computational focus with no prerequisite knowledge of geometry and topology assumed.)

• Analytic Combinatorics in Several Variables (2nd Edition) by Robin Pemantle, Mark C. Wilson, and Stephen Melczer. Cambridge University Press, 2023. (The most complete and expansive treatment of the theory for researchers, making use of stratified Morse theory to present a comprehensive framework for studying multivariate generating functions. The first edition came out in 2013.)

and those wanting to see further examples illustrating the theory can consult

The following list of papers is updated on an ongoing basis and listed in reverse chronological order.

1. Stationary points at infinity for analytic combinatorics by Yuliy Baryshnikov, Stephen Melczer and Robin Pemantle. To appear in Foundations of Computational Mathematics.

2. Asymptotics of multivariate sequences in the presence of a lacuna by Yuliy Baryshnikov, Stephen Melczer and Robin Pemantle. Under review 2021.

3. Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems by Stephen Melczer and Bruno Salvy. Journal of Symbolic Computation, Volume 103, 234–279, 2021.

4. Asymptotics of Bivariate Generating Functions with Algebraic Singularities by Torin Greenwood. J. Combinatorial Theory A, 2018.

5. Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration by Stephen Melczer. PhD thesis (Waterloo/Lyon), 259 pages, 2017.

6. Automatic asymptotics for coefficients of smooth, bivariate rational functions by Timothy DeVries, Joris van der Hoeven and Robin Pemantle. Online J. Anal. Comb., vol. 6, 24 pages (2012).

7. New software for computing asymptotics of multivariate generating functions by Alexander Raichev. ACM Communications in Computer Algebra 45 (2011), 183-185.

8. Asymptotics of coefficients of multivariate generating functions: improvements for smooth points by Alexander Raichev and Mark C. Wilson. Online Journal of Analytic Combinatorics, 2011.

9. Analytic combinatorics in $d$ variables: An overview by Robin Pemantle. AMS Contemporary Mathematics 520, 2010.

10. A case study in bivariate singularity analysis by Timothy Devries. AMS Contemporary Mathematics 520, 2010.

11. Asymptotic expansions of oscillatory integrals with complex phase by Robin Pemantle and Mark C. Wilson. AMS Contemporary Mathematics 520.

12. Asymptotics of multivariate sequences, part III: Quadratic points by Yuliy Baryshnikov and Robin Pemantle. Advances in Mathematics 228 (2011), 3127-3206.

13. Asymptotics of coefficients of multivariate generating functions: improvements for smooth points by Alexander Raichev and Mark C. Wilson. Electron. J. Combin. 15 (2008), no. 1, Research Paper 89, 17 pp.

14. A new method for computing asymptotics of diagonal coefficients of multivariate generating functions by Alexander Raichev and Mark C. Wilson. Proceedings of International Conference on Analysis of Algorithms, Juan-les-Pins, 2007.

15. Uniform formulae for coefficients of meromorphic functions in two variables. Part I by Manuel Lladser. SIAM Journal on Discrete Mathematics 20 (2007), 811-828.

16. Mixed powers of generating functions by Manuel Lladser. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, Discrete Mathematics and Theoretical Computer Science Proceedings, AG, 171-182, 2006.

17. Asymptotics for generalized Riordan arrays by Mark C. Wilson. Discrete Mathematics and Theoretical Computer Science, volume AD (2005), 323-334 (Proceedings of the 2005 International Conference on Analysis of Algorithms, Barcelona).

18. Convolutions of inverse linear functions via multivariate residues by Yuliy Baryshnikov and Robin Pemantle. Preprint (2004), 42 pages.