Rainbow 3-term arithmetic progressions.
Ramanujan identities and Euler products for a type of Dirichlet series
Ramanujan type trigonometric formulas: the general form for the argument .
Ramsey problems in additive number theory
Random sets and additive bases in .
Range of density measures
We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...
Rational identities and inequalities.
Rational identities and inequalities involving Fibonacci and Lucas numbers.
Rational tree morphisms and transducer integer sequences: definition and examples.
Reading along arithmetic progressions
Given a 0-1 sequence x in which both letters occur with density 1/2, do there exist arbitrarily long arithmetic progressions along which x reads 010101...? We answer the above negatively by showing that a certain regular triadic Toeplitz sequence does not have this property. On the other hand, we prove that if x is a generalized binary Morse sequence then each block can be read in x along some arithmetic progression.
Rearrangements of the Symmetric Group and Enumerative Properties of the Tangent and Secant Numbers.
Recherches sur la divisibilité du nombre par les puissances de la factorielle
Reciprocity formulae for general multiple Dedekind-Rademacher sums and enumeration of lattice points
Reciprocity laws for generalized higher dimensional Dedekind sums
We define a class of generalized Dedekind sums and prove a family of reciprocity laws for them. These sums and laws generalize those of Zagier [6]. The method is based on that of Solomon [5].
Reconstructing integer sets from their representation functions.
Recounting determinants for a class of Hessenberg matrices.
Recouvrement optimal du cercle par les multiples d'un intervalle
Rectangular and trapezoidal arrangements.
Recurrence formulae for multi-poly-Bernoulli numbers.
Récurrences - et -mahlériennes
On sait (Cobham) qu’une suite - et -automatique est une suite rationnelle. Une question de Loxton et van der Poorten étend ce résultat au cas - et -régulier. On montre dans cet article que, si une suite vérifie une récurrence - et -mahlérienne d’ordre un, elle est rationnelle.