9 papers
On Periodic and Aperiodic Optimal Strategies in Solvency Games
Quentin Guilmant, Florian Luca, Richard Mayr +2
Solvency games are a gambling problem on infinite-state Markov decision processes in which the state represents an investor's fortune. In every round, the invest…
On the Divisibility Relation and a Generalized Erdős--Sierpiński Conjecture
Amirali Fatehizadeh, Florian Luca
For each fixed positive integer , we study the divisibility relation . We isolate an explicit regular family arising from integral quotients of shifted abundancy…
Multiplicative dependence in the sumset of multiplicative groups
Yuri Bilu, Florian Luca
Let and be finitely generated multiplicative groups of algebraic numbers such that is a finite group. We show that, up to finitely many exceptions, non-zero sums $…
Conjectural Decidability of the Skolem Problem
Florian Luca, Joël Ouaknine, James Worrell
The Skolem Problem asks to determine whether a given integer linear recurrence sequence (LRS) has a zero term. This problem, whose decidability has been open for many decades, aris…
On the growth of hypergeometric sequences
George Kenison, Jakub Konieczny, Florian Luca +3
Hypergeometric sequences obey first-order linear recurrence relations with polynomial coefficients and are commonplace throughout the mathematical and computational sciences. For c…
Transcendence of Hecke-Mahler Series
Florian Luca, Joel Ouaknine, James Worrell
We prove transcendence of the Hecke-Mahler series , where is a non-constant polynomial is a real numbe…
On the Decidability of Presburger Arithmetic Expanded with Powers
Toghrul Karimov, Florian Luca, Joris Nieuwveld +2
We prove that for any integers , the existential fragment of the first-order theory of the structure …
Transcendence for Pisot Morphic Words over an Algebraic Base
Pavol Kebis, Florian Luca, Joel Ouaknine +2
It is known that for a uniform morphic sequence and an algebraic number such that , the number $[\![\boldsymbol{u} ]\!]…
Twisted rational zeros of linear recurrence sequences
Yuri Bilu, Florian Luca, Joris Nieuwveld +2
We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rat…