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.
Recurrences and Legendre transform.
Recurrences for the Bernoulli and Euler numbers.
Recurrent versus diffusive dynamics for a kicked quantum oscillator
Reducibility and irreducibility of Stern -polynomials
The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and we state a...
Reducing a set by subtracting squares.
Regular coverings of the integers by arithmetic progressions