On zero-sum sequences in .
On zero-sum subsequences in finite Abelian groups.
One pile Nim with arbitrary move function.
One property of triangular numbers.
Opérations sur les mots de Christoffel
On peut définir la pente d'un mot écrit avec des 0 et des 1 comme le nombre de 1 divisé par le nombre de 0, et généraliser cette définition aux mots de longueur infinie. Considérant le lien entre les mots de Christoffel et les fractions continues, on se propose d'étudier le comportement de tels mots lorsqu'on additionne leurs pentes, ou qu'on les multiplie par un entier positif. Après un bref exposé des différentes notions liées aux mots de Christoffel, l'étude de la somme et de la multiplication...
Optimal bounds for the length of rational Collatz cycles
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...
Orthogonal systems in vector spaces over finite fields.
Orthogonality and the maximum of Littlewood cosine polynomials
Oscillatory nonautonomous Lucas sequences.
-adic analysis and Bell numbers of two variables. (Analyse -adique et nombres de Bell à deux variables.)
p-adic Dedekind sums.
p-adic valuations of some sums of multinomial coefficients
Padovan and Perrin numbers as products of two generalized Lucas numbers
Let and be the -th Padovan and Perrin numbers respectively. Let be non-zero integers with and , let be the generalized Lucas sequence given by , with and In this paper, we give effective bounds for the solutions of the following Diophantine equations where , and are non-negative integers. Then, we explicitly solve the above Diophantine equations for the Fibonacci, Pell and balancing sequences.
Padua and Pisa are exponentially far apart.
We answer the question posed by Ian Stewart which Padovan numbers are at the same time Fibonacci numbers. We give a result on the difference between Padovan and Fibonacci numbers, and on the growth of Padovan numbers with negative indices.
Parallelepipeds, nilpotent groups and Gowers norms
In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions and and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.
Parity theorems for statistics on domino arrangements.
Partial Bell polynomials and inverse relations.
Partial complements and transposable dispersions.
Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal form.