D-Finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic

A special session at ACA 2023, Warsaw, Poland, July 17–21, 2023.

Organizers

• Shaoshi Chen (Chinese Academy of Sciences, China)
• Frédéric Chyzak (Inria, France)
• Antonio Jiménez-Pastor (Aalborg University, Denmark)
• Manuel Kauers (Johannes Kepler University Linz, Austria)
• Veronika Pillwein (Johannes Kepler University Linz, Austria)

Aim and Scope

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 session that took place in 2022.

Confirmed Speakers

• Florent Bréhard (U. Lille, Lille, France): A symbolic-numeric validation algorithm for linear ODEs with Newton-Picard method [abstract|slides]
• Hadrien Brochet (Inria, Palaiseau, France): Reduction based creative telescoping for definite summation of P-recursive sequences: the Lagrange identity approach [abstract|slides]
• Manfred Buchacher (RICAM, Linz, Austria): Separating variables in bivariate polynomial ideals: the local case [abstract]
• Lixin Du (JKU, Linz, Austria): Reduction-based creative telescoping for definite summation of P-recursive sequences: the integral-basis approach [abstract|slides]
• Qing-hu Hou (Tianjin University, Tianjin, China): Two applications of the telescoping method [abstract|slides]
• Philipp Nuspl (RISC, Linz, Austria): Linear recurrence sequences in the OEIS [abstract|slides]
• Georg Regensburger (U. Kassel, Kassel, Germany): Algebraic consequences of the fundamental theorem of calculus in differential rings [abstract|slides]
• Catherine St-Pierre (Inria, Palaiseau, France): How a linear recurrence problem inspired a solution in algebraic geometry [abstract|slides]
• Armin Straub (U. South Alabama, Mobile, USA): Automatic Lucas-type congruences [abstract|slides]

Program

See the pdf program accessible by a link from the conference main website (on page 6 at the time of writing).