A note on universal Hilbert sets.
A note on univoque self-sturmian numbers
We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number in is univoque and self-sturmian if and only if the -expansion of is of the form , where is a characteristic...
A note on univoque self-Sturmian numbers
We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic...
A notion of density and essential components in GF[p,x]
A number-theoretic conjecture and its implication for set theory.
A -adic study of the partial sums of the harmonic series.
A partition formula for Fibonacci numbers.
A partition identity with certain applications
A partition of the non-negative integers, with applications.
A permutations representation that knows what “Eulerian” means.
A polynomial investigation inspired by work of Schinzel and Sierpiński
A polynomial related to the cyclotomic polynomial
A problem of Diophantos-Fermat and Chebyshev polynomials of the second kind.
A problem of Erdős-Szüsz-Turán on diophantine approximation
A problem of Rankin on sets without geometric progressions
A geometric progression of length k and integer ratio is a set of numbers of the form for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence of positive real numbers with a₁ = 1 such that the set contains no geometric progression of length k and integer ratio. Moreover, is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that there is...
A product theorem for Skolem sequences.
A proof of a conjecture of Knuth.
A proof of Pisot's th root conjecture.
A proof of the identities of Gordon and MacMahon and two new identities. (La démonstration des identités de Gordon et MacMahon et de deux identités nouvelles.)
A propos de la fonction d’Erdös et Graham
Nous améliorons les meilleures bornes supérieures et inférieures connues pour la fonction d’Erdös et Graham définie par , où le premier maximum est pris sur toutes les bases (exactes) d’ordre au plus , où désigne le sous-ensemble de composé des éléments tels que soit encore une base et où, enfin, désigne l’ordre (exact) de . Notre étude nous conduira, entre autres, à prouver un nouveau résultat additif général découlant de la méthode isopérimétrique et à étudier trois problèmes additifs...