SS8 - D-Finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic
link to the session's webpage
D-finite functions are solutions of linear differential equations with rational function coefficients. They form an important class of special functions that appears ubiquitously in algebra, combinatorics, number theory, and beyond. The class is closed under addition and multiplication, derivation and integration, various kinds of coefficient extraction, and under taking diagonals of series. The D-finiteness of generating functions also reflects the complexity of combinatorial classes, with definite relevance in enumeration. This has long made D-finite functions become a standard data structure for the manipulation of special functions in symbolic computation and combinatorics. D-finite functions also admit several extensions amenable to more recent algorithmic treatments, such as DD-finite functions and series defined by quadratic differential equations.
The goal of this special session is to create an exchanging forum for researchers who work on the algorithmic, combinatorial, and arithmetic aspects of D-finite and related functions. It is a continuation of the special sessions that took place in 2022 and 2023.
Session organizers
| Shaoshi Chen (Chinese Academy of Sciences, China) |
| Frédéric Chyzak (Inria, France) |
| Antonio Jiménez-Pastor (Universidad Politécnica de Madrid, Spain) |
| Manuel Kauers (Johannes Kepler University Linz, Austria) |
| Veronika Pillwein (Johannes Kepler University Linz, Austria) |
Talks
| Shachar Weinbaum - Conservative Matrix Fields - Algebra and Asymptotics |
| Ali K. Uncu - A MacMahon Partition Analysis View of Cylindric Partitions |
| Frédéric Chyzak - Computing D-Finite Symmetric Scalar Products in Order to Count Regular Graphs |
| Julien Roques - A purity theorem for Mahler equations |
| Bertrand Teguia Tabuguia - Guessing and arithmetic of D-algebraic sequences |
| Georg Regensburger - Integro-differential rings and generalized shuffle relations |
| Jakob Obrovsky - A direct solver for coupled systems of recurrence equations over ΠΣ∗-fields |
| Manuel Kauers - Non-Minimality of Minimal Telescopers Explained by Residues |