Research

Below is a listing of my publications, invited talks, academic service, and similar things.
Click the Cite button below a publication to retrieve its bibtex entry.

Books

Robin Pemantle, Mark C. Wilson, Stephen Melczer (2024). Analytic Combinatorics in Several Variables, 2nd Edition. Cambridge Studies in Advanced Mathematics, Cambridge University Press.

Book Webpage and Manuscript

Stephen Melczer (2021). An Invitation to Analytic Combinatorics: From One to Several Variables. Springer Texts & Monographs in Symbolic Computation.

Book Website and Manuscript Publisher Website

Submitted

Alexander Kroitor, Stephen Melczer (2023). Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant. Submitted.

arXiv Version

Jeremy Chizewer, Stephen Melczer, J. Ian Munro, Ava Pun (2023). Enumeration and Succinct Encoding of AVL Trees. Submitted.

arXiv Version

Journal Articles

Stephen Melczer, Tiadora Ruza (2024). Central Limit Theorems via Analytic Combinatorics in Several Variables. Accepted to Electronic Journal of Combinatorics.

arXiv Version Code

Ruiwen Dong, Stephen Melczer, Marc Mezzarobba (2024). Computing Error Bounds for Asymptotic Expansions of Regular P-Recursive Sequences. Mathematics of Computation, Volume 93, 977–1017.

Journal Version arXiv Version

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle (2024). Asymptotics of multivariate sequences in the presence of a lacuna. Accepted to Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions.

Journal Version arXiv Version

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle (2024). Asymptotics of multivariate sequences IV: generating functions with poles on a hyperplane arrangement. Annals of Combinatorics, Volume 28, 169–221.

Journal Version arXiv Version Code

Stephen Melczer, Marc Mezzarobba (2022). Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes. Combinatorial Theory, Volume 2(2), Paper 4, 20p.

Journal Version arXiv Version Code

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle (2022). Stationary points at infinity for analytic combinatorics. Foundations of Computational Mathematics, Volume 22(5), 1631–1664.

Journal Version arXiv Version Code

Stephen Melczer, Marcus Michelen, Somabha Mukherjee (2021). Asymptotic bounds on graphical partitions and partition comparability. International Mathematics Research Notices, Volume 2021(4), 2842–2860.

Journal Version arXiv Version

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

Journal Version arXiv Version Maple Code

Jessica Khera, Erik Lundberg, Stephen Melczer (2021). Asymptotic Enumeration of Lonesum Matrices. Advances in Applied Mathematics, Volume 123, 102–118.

Journal Version arXiv Version

Alin Bostan, Mireille Bousquet-Mélou, Stephen Melczer (2021). Counting walks with large steps in an orthant. Journal of the European Mathematical Society, Volume 23 (7), 2221–2297.

Journal Version arXiv Version Code

Stephen Melczer, Greta Panova, Robin Pemantle (2020). Counting Partitions inside a Rectangle. SIAM Journal on Discrete Mathematics, Volume 34(4), 2388–2410.

Journal Version arXiv Version

Stephen Melczer, Marni Mishna, Robin Pemantle (2020). Combinatorial Adventures in Analysis, Algebra, and Topology. Notices of the American Mathematical Society, Volume 67(2), 262–265.

Journal Version

Stephen Melczer, Mark C. Wilson (2019). Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior. SIAM Journal on Discrete Mathematics, Volume 33(4), 2140–2174.

Journal Version arXiv Version

Veronika Irvine, Stephen Melczer, Frank Ruskey (2019). Vertically constrained Motzkin-like paths inspired by bobbin lace. Electronic Journal of Combinatorics, Volume 26(2), P2.16.

Journal Version arXiv Version

Seung Gyu Hyun, Stephen Melczer, Catherine St-Pierre (2019). A Fast Algorithm for Solving Linearly Recurrent Sequences. ACM Communications in Computer Algebra, Volume 52(3), 100–103.

Journal Version arXiv Version

Julien Courtiel, Stephen Melczer, Marni Mishna, Kilian Raschel (2017). Weighted lattice walks and universality classes. Journal of Combinatorial Theory, Series A, Volume 152, 255–302.

Journal Version arXiv Version

Sophie Burrill, Julien Courtiel, Eric Fusy, Stephen Melczer, Marni Mishna (2016). Tableau sequences, open diagrams, and Baxter families. European Journal of Combinatorics, Volume 58, 144–165.

Journal Version arXiv Version

Alin Bostan, Mireille Bousquet-Mélou, Manuel Kauers, Stephen Melczer (2016). On 3-dimensional lattice walks confined to the positive octant. Annals of Combinatorics, Volume 20(4), 661–704.

Journal Version arXiv Version

Stephen Melczer, Marni Mishna (2016). Asymptotic lattice path enumeration using diagonals. Algorithmica, Volume 75(4), 782–811.

Journal Version arXiv Version Extended Abstract

Stephen Melczer, Marni Mishna (2014). Singularity analysis via the iterated kernel method. Combinatorics, Probability, and Computing, Volume 23(5), 861–888.

Journal Version arXiv Version Extended Abstract

Proceedings Papers

Benjamin Hackl, Andrew Luo, Stephen Melczer, Jesse Selover, Elaine Wong (2023). Rigorous Analytic Combinatorics in Several Variables in SageMath. Séminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2023, Volume 89B, Article 90, 12p.

FPSAC links arXiv Version GitHub

Andreas Lenz, Stephen Melczer, Cyrus Rashtchian, Paul H. Siegel (2023). Exact Asymptotics for Discrete Noiseless Channels. 2023 IEEE International Symposium on Information Theory (ISIT).

Journal Version

Kisun Lee, Stephen Melczer, Josip Smolčić (2022). Homotopy Techniques for Analytic Combinatorics in Several Variables. Proceedings of the 24th International Symposium SYNASC, 27–34.

Journal Version arXiv Version Julia package

Torin Greenwood, Stephen Melczer, Tiadora Ruza, Mark C. Wilson (2022). Asymptotics of coefficients of algebraic series via embedding into rational series. Séminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2022, Volume 86B, Article 30, 12p.

Journal Version arXiv Version

Seung Gyu Hyun, Stephen Melczer, Éric Schost, Catherine St-Pierre (2019). Change of Basis for M-primary Ideals in One and Two Variables. Proceedings of the ACM on ISSAC 2019, 227–234.

Journal Version arXiv Version

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle, Armin Straub (2018). Diagonal asymptotics for symmetric rational functions via ACSV. LIPIcs Proceedings of Analysis of Algorithms, Volume 110, 1–12:15.

Published Version arXiv Version

Stephen Melczer, Mark C. Wilson (2016). Asymptotics of lattice walks via analytic combinatorics in several variables. DMTCS Proceedings of FPSAC 2016, 863–874.

Published Version arXiv Version

Stephen Melczer, Bruno Salvy (2016). Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables. Proceedings of the ACM on ISSAC, 333–340.

Journal Version arXiv Version

Sophie Burrill, Stephen Melczer, Marni Mishna (2015). A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape. DMTCS proceedings of FPSAC 2015, 369–380.

Published Version arXiv Version

Marzieh Bayeh, Erin Compaan, Theodore Lindsey, Nathan Orlow, Stephen Melczer, Zachary Voller (2014). Ink-constrained halftoning with application to QR codes. Proceedings of the SPIE, Volume 9015, 90150U–90150U-8.

Journal Version

Lecture Notes

Stephen Melczer (2023). An Invitation to Enumeration (enumeration.ca).

Link to Notes

Thesis

Stephen Melczer (2017). Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration. PhD Thesis for ENS Lyon and University of Waterloo.

arXiv Version Waterloo Link ENS Link Code

See also my complete arXiv listing and my OrcID page

Selected Invited Talks

Event / Institute Location Session / Workshop Date
Formal Power Series and Algebraic Combinatorics (FPSAC) Sapporo, Japan Plenary Speaker July 2025
Henri Poincaré Institute (IHP) Paris Workshop on Computer Algebra for Functional Equations in Combinatorics and Physics December 2023
Mathematical Summer in Paris Paris Lecture and Exercise Session on Analytic Combinatorics June 2023
Banff International Research Station (BIRS) Banff Workshop on Analytic and Probabilistic Combinatorics November 2022
American Institute of Mathematics (AIM) San Jose Workshop on Analytic Combinatorics in Several Variables April 2022
AMS Joint Math Meeting Seattle Special Session on Combinatorial Applications of Computational Geometry and Algebraic Topology April 2022
Centre International de Rencontres Mathématiques (CIRM) Marseille Luminy ALEA Days Mini-Course March 2022
Mathematical Congress of the Americas Buenos Aires Symbolic Computation: Theory, Algorithms and Applications July 2021
Centre International de Rencontres Mathématiques (CIRM) Marseille Luminy Lattice Paths and Interactions June 2021
Séminaire Philippe Flajolet Institut Henri Poincaré April 2021
SIAM-CAIMS Joint Annual Meeting Toronto Symbolic Computation and Special Functions Canceled by CoVID
Foundations of Computational Mathematics Vancouver Graph Theory and Combinatorics Canceled by CoVID
Banff International Research Station (BIRS) Alberta Asymptotic Algebraic Combinatorics March 2019
AMS/MAA Joint Math Meeting Baltimore AMS Session on Enumerative Combinatorics January 2019
Research Institute for Symbolic Computation / JKU Linz Linz, Austria Algorithmic and Enumerative Combinatorics Summer School July 2018
Ontario Research Centre for Computer Algebra University of Western Ontario May 2018
Tutte Colloquium University of Waterloo April 2018
AMS/MAA Joint Math Meeting San Diego AMS Session on Applied and Computational Combinatorics January 2018
Erwin Schrödinger Institute Vienna Programme on Algorithmic and Enumerative Combinatorics November 2017
SIAM Conference on Applied Algebraic Geometry Georgia Tech, Atlanta New Trends in Polynomial System Solving Minisymposium August 2017
Journées de combinatoire de Bordeaux Laboratoire Bordelais de Recherche en Informatique (LaBRI) January 2016
Fields Institute Thematic Program on Computer Algebra Toronto Workshop on Symbolic Combinatorics and Computational Differential Algebra September 2015
SIAM Conference on Applied Algebraic Geometry Colorado State, Fort Collins Symbolic Combinatorics Minisymposium August 2013

Academic Service

AofA 2025 Organizing Committee Co-Chair, Ontario
36th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms

CIRM 2025 Conference Organizing Committee, Marseille-Luminy
Enumerative combinatorics and effective aspects of differential equations
Part of the Singularities, differential equations and transcendence thematic month in February 2025

AofA 2024 Program Committee, Bath UK
35th Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms

FPSAC 2023 Program Committee, UC Davis
35th International Conference on Formal Power Series and Algebraic Combinatorics

SIAM Applied Algebraic Geometry 2023 Minisymposium Co-organizer, Eindhoven
Symbolic Combinatorics (Contributed Minisymposium)
With Shaoshi Chen and Manuel Kauers

AofA 2022 Program Committee, Philadelphia
33rd Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms

SIAM Applied Algebraic Geometry 2021 Minisymposium Co-organizer, Texas A&M
Symbolic Combinatorics (Contributed Minisymposium)
With Shaoshi Chen and Manuel Kauers

CanaDAM 2021 Minisymposium Organizer, Virtual
New Trends in Analytic Combinatorics (Contributed Minisymposium)

AMS Mathematics Research Community 2021 Co-organizer, Rhode Island
Combinatorial Applications of Computational Topology and Algebraic Geometry
With Marni Mishna and Robin Pemantle

ISSAC 2019 Poster Program Committee, Beijing, China
44th International Symposium on Symbolic and Algebraic Computation (ISSAC)

SIAM Applied Algebraic Geometry 2019 Minisymposium Co-organizer, Bern, Switzerland
Symbolic Combinatorics (Contributed Minisymposium)
With Shaoshi Chen and Manuel Kauers

International Congress of Mathematical Software 2018 Program Committee
Session Chair and Organizer, Symbolic Combinatorics
University of Notre Dame, South Bend, Indiana

2017 BIRS Workshop Co-organizer, Banff, Alberta
Lattice walks at the Interface of Algebra, Analysis, and Combinatorics
With Mireille Bousquet-Mélou, Marni Mishna, and Michael Singer

SIAM Applied Algebraic Geometry 2017 Minisymposium Co-organizer, Georgia Tech
Symbolic Combinatorics (Contributed Minisymposium)
With Shaoshi Chen, Manuel Kauers, and Michael Singer

FPSAC 2016 Organizing Committee, Simon Fraser University, Vancouver
28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC)

CanaDAM 2015 Minisymposium Organizer, University of Saskatchewan
Automated analysis of combinatorial structures (Contributed Minisymposium)

External Grant Reviewer: Natural Sciences and Engineering Research Council of Canada (NSERC) and Austrian Science Fund (FWF)

Referee: Transactions of the AMS, Combinatorial Theory, Annals of Combinatorics, Electronic Journal of Combinatorics, The Ramanujan Journal, Applied Algebra in Engineering, Communication & Computing, Discrete Mathematics, Theoretical Computer Science, Online Journal of Analytic Combinatorics, Graphs and Combinatorics, Journal of Integer Sequences, Proceedings of the ACM on ISSAC, Proceedings of FPSAC, Proceedings of Analysis of Algorithms (AofA), Proceedings of the International Congress of Math Software, Reviewer for Mathematical Reviews

University Service at Waterloo includes (over different time periods) organizing the Tutte Colloquium, organizing the Algebraic and Enumerative Combinatorics seminar, enumeration course redevelopment, and setting the Enumeration PhD Comprehensive exam.

Selected Seminar Presentations

Seminar Location Date
Séminaire Combinatoire et Informatique du LaCIM Montreal March 2023
Waterloo Algorithms and Complexity Seminar Waterloo August 2022
UVic Combinatorics Seminar Victoria October 2021
AriC / LIP Computing Seminar Lyon December 2020
UMass Amherst Discrete Math Seminar Amherst MA March 2020
Drexel University Analysis Seminar Philadelphia April 2019
University of Toronto Probability Seminar Toronto January 2019
University of Toronto CS Theory Group Seminar Toronto October 2018
Courant-CUNY Kolchin Seminar in Differential Algebra New York September 2018
Waterloo Algebraic Combinatorics Seminar Waterloo August 2018
Hofstra University Mathematics Seminar Long Island April 2018
SFU Discrete Math and Computer Algebra Seminars Vancouver March 2018
University of Illinois Probability Seminar Urbana-Champaign January 2018
University of Delaware Probability Seminar Newark DE November 2017
Penn/Temple Probability Seminar Philadelphia October 2017
Philadelphia Combinatorics, Algebra, and Geometry Seminar Philadelphia September 2017
University of Waterloo Symbolic Computation Seminar Waterloo May 2017
UCLA Combinatorics Seminar Los Angeles January 2017
York University Applied Algebra Seminar Toronto January 2017
University of Carleton Combinatorics Seminar Ottawa October 2016
SpecFun Computations and Proofs Seminar École Polytechnique June 2016
RISC Algorithmic Combinatorics Seminar Hagenberg June 2016
Arithmetic and Computing Seminar ENS Lyon June 2016
Seminar Algebra und Diskrete Mathematik JKU Linz June 2016
Combinatoire et Théorie des Nombres, Institut Camille Jordan Lyon October 2015
LaBRI Séminaire de Combinatoire Bordeaux October 2015
LIPN Séminaire de combinatoire Paris December 2012
Inria - Microsoft Research Joint Lab Seminar École Polytechnique October 2012
LIAFA Séminaire Université Paris 7 Diderot October 2012
INRIA Algorithms Seminar Université Paris 11 May 2012