ACA 2017 Session: Algorithmic Combinatorics

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Organizer

Christoph Koutschan (RICAM, Austrian Academy of Sciences)

Aims and Scope

The interplay between computer algebra and combinatorics has been very fruitful for quite a while 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 kind of lattice walks, the study of symmetry classes of plane partitions, various types of tiling problems in the plane, the counting of lattice points in polytopes and the computation of Ehrhart polynomials, graph theory, and pattern avoidance in permutations; many of these concepts are employed in other research areas as well, for example in physics. There are numerous ways in which 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
evaluation of binomial sums, as well as more general sums and integrals, by means of the Wilf-Zeilberger algorithmic proof theory
creative telescoping algorithms
symbolic summation and integration techniques
(q-) difference and differential equations: construction of explicit solutions and investigation of structural properties
fast numerical evaluation of combinatorial sequences and special functions, e.g. at high precision
hypergeometric series
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 session will result in a vivid exchange of ideas and that it will foster future collaborations and interactions.

Speakers

Giora Dula: Computing automorphism groups of designs — a way to produce new symmetric weighing matrices (abstract, slides)
Assaf Goldberger: Reconstructing weighing matrices from their automorphism group (abstract)
Chaim Even-Zohar: Patterns in random permutations (abstract)
Hui Huang: D-finite numbers (abstract, slides)
Manuel Kauers: Bounds for D-finite substitution (abstract, slides)
Lin Jiu: Bernoulli symbol on multiple zeta values at negative integers (abstract)
Thotsaporn Thanatipanonda: Time for the new ansatz (?) (abstract, slides)
Andrzej Kisielewicz: Algorithmic aspects of the Černý conjecture (abstract)
Ilias S. Kotsireas: Algorithms and open problems for weighing matrices (abstract)
Toufik Mansour: Wilf classification of subsets of four-letter patterns (abstract, slides)
Eric Rowland: Automatic proofs for establishing the structure of integer sequences avoiding a pattern (abstract, slides)
Malka Schaps: External Littelmann paths for crystals of type A (abstract, slides)
Mee Seong Im: The category of finite-dimensional representations of periplectic Lie superalgebras (abstract, slides)
Liangjie Ye: Computer algebra algorithms for proving Jacobi theta function identities (abstract)
Yi Zhang: Apparent singularities of D-finite systems (abstract, slides)

Call for Contributions

If you are interested in presenting your recent work in this session, please send your title and abstract to Christoph Koutschan, no later than April 30, 2017; see the section important dates on the ACA homepage. Please use the LaTeX template for your submission, see the page ACA 2017 Publications for detailed instructions. Your abstract should be 1–2 pages long, including references.