Organizers
Miklos Bona (University of Florida, USA)
Ilias Kotsireas (Wilfred Laurier University, CA & Athena RC, GR)
Ali K. Uncu (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, AT & University of Bath, UK)
Aims and Scope
The interplay between computer algebra and combinatorics has been very fruitful for many years. There are two main pillars to this relation: algorithms to carry out heavy and error-prone calculations to aid proof and experiments and sampling data to make new conjectures. We can represent these under the name "algorithmic combinatorics" and “experimental combinatorics”, respectively. Nowadays both are well-established research areas. 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 to formulate or support conjectures
manipulation of generating functions, such as executing D-finite closure properties, extracting coefficients, or determining the asymptotic behavior
(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.
Currently, both algorithmic and experimental combinatorics are 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.
Curtis Bright (University of Windsor, CA) - Abstract (online talk)
Yasemin Büyükçolak (Gebze Technical University, TR) - Abstract
Shaoshi Chen (Chinese Academy of Sciences, CN) - Abstract
Shane Chern (Dalhouse University, CA) - Abstract
Atul Dixit (IIT Gandhinagar, IN) - Abstract
Nikolai Fadeev (Research Institute for Symbolic Computation, JKU Linz, AT) - Abstract
Rajat Gupta (Institute of Mathematics, Academia Sinica, TW) - Abstract (online talk)
Hui Huang (Dalian University of Technology, CN)- Abstract (online talk)
Antonio Jimenez-Pastor (Laboratoire d'Informatique de l'Ecole Polytechnique, FR) - Abstract
Pietro Mercuri (Universita Sapienza, IT) - Abstract
Halime Ömrüuzun Seyrek (Sabanci University, TR) - Abstract
Nicolas Smoot (Research Institute for Symbolic Computation, JKU Linz, AT) - Abstract (online talk)
Henning Ulfarsson (Reykjavík University, IS) - Abstract
Vince Vatter (University of Florida, US) - Abstract
Ae Ja Yee (Pennsylvania State University, US) - Abstract (online talk)
Fatih Yetgin (Gebze Technical University, TR) - Abstract
Emre Yivli (Eskişehir Technical University, TR) - Abstract
Mohammad Zadeh Dabbagh (Sabanci University, TR) - Abstract
Doron Zeilberger (Rutgers University, US) - Abstract
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 30, 2022. Please use the LaTeX template for your submission.