3 papers
math.CO2024
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
math.CA2021
Differential Galois Theory and Integration
Thomas Dreyfus, Jacques-Arthur Weil
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illus…
math.NT2018
Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
Carlos E. Arreche, Thomas Dreyfus, Julien Roques
We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular…