ACA 2021 Session: Algorithmic Combinatorics

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Organizers

• Hao Du (School of Sciences, Beijing University of Posts and Telecommunications, China)
• Christoph Koutschan (RICAM, Austrian Academy of Sciences, Linz)
• Ali Uncu (University of Bath, United Kingdom)

Aims and Scope

The interplay between computer algebra and combinatorics has been very fruitful for many years and can be subsumed under the name "algorithmic combinatorics", which nowadays is a well-established research area. It is one of the many success stories concerning the applications of computer algebra, and it perfectly demonstrates how two scientific disciplines can interact and inspire each other: on the one hand, combinatorialists appreciate the power of computer algebra systems, and on the other hand, problems from combinatorics are one of the driving forces for the development of new computer algebra algorithms and packages.

Examples include the enumeration of different types of lattice walks, the study of symmetry classes of plane partitions and alternating sign matrices, various types of tiling problems in the plane, the counting of lattice points in polytopes and the computation of Ehrhart polynomials, partition analysis and q-identities, graph theory, and pattern avoidance questions. There are numerous ways in which experimental mathematics, and specifically computer algebra, can contribute to these problem areas:

• generation of experimental data in order to formulate or support conjectures
• manipulation of generating functions, such as executing D-finite closure properties, extracting coefficients, or determining the asymptotic behaviour
• (q-) difference and differential equations: construction of explicit solutions and investigation of structural properties
• evaluation of binomial sums, as well as more general sums and integrals, by means of the Wilf-Zeilberger algorithmic proof theory
• fast and/or high-precision numerical evaluation of combinatorial sequences and special functions
• hypergeometric series: identities, evaluation, asymptotics
• symbolic evaluation of determinants and Pfaffians related to counting problems
• etc. etc.

Currently, algorithmic combinatorics is a very active research area, and we hope that this special session will result in a vivid exchange of ideas and that it will foster future collaborations and interactions.

Confirmed Speakers

• Matthias Beck: Rational Ehrhart Theory (abstract, slides)
• Shaoshi Chen: Separability Problems in Creative Telescoping (abstract, slides)
• Hui Huang: Constructing Minimal Telescopers for Rational Functions in Three Discrete Variables (abstract, slides)
• Manuel Kauers: Quadrant Walks Starting Outside the Quadrant (abstract, slides)
• Kağan Kurşungöz: A Combinatorial Construction for Two Formulas in Slater's List (abstract, slides)
• Haggai Liu: Enumerative Properties of Cogrowth Series on Free Products of Finite Groups (abstract, slides)
• Jay Pantone: Combinatorial Exploration: A New Approach to Enumeration (abstract, slides)
• Eric Rowland: The Size of the Minimal Automaton for an Algebraic Sequence (abstract, slides)
• Ali Uncu: The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition (abstract, slides)
• Elaine Wong: Binomial Determinants for Tiling Problems Yield to the Holonomic Ansatz (abstract, slides)
• Ae Ja Yee: Combinatorics of Truncated Partition Theorems (abstract, slides)
• Sergey Yurkevich: Diagonals and Hypergeometric Functions (abstract, slides)

Call for Contributions

If you are interested in presenting your recent work in this session, please send your title and abstract to one of the session organizers, no later than May 23, 2021. Please use the LaTeX template for your submission.

ACA 2021 post-proceedings will be published in the Springer series Springer Proceedings in Mathematics & Statistics. Full papers (up to 20 pages) corresponding to the talks presented at the ACA 2021 special sessions can be submitted for publication to the Springer Proceedings volume; these contributions will be refereed.

Selected papers presented at ACA 2021 will be invited to submit a revised version for publication in Springer's Mathematics in Computer Science journal and Springer's Applicable Algebra in Engineering, Communication and Computing journal. More details, regarding the requirements of the revised papers, eligibility and guest editors will be announced soon here.