Additional Fibonacci-Bernoulli relations

Congruences Involving Combinations of the Bernoulli and Fibonacci Numbers.

Tiling Proofs of Some Fibonacci-lucas Relations

We provide tiling proofs for some relations between Fibonacci and Lucas numbers, as requested by Benjamin and Quinn in their text, Proofs that Really Count. Extending our arguments yields Gibonacci generalizations of these identities.

Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials

In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, and present several new recurrence relations for the Bernoulli numbers and polynomials.

Some Relations Between Generalized Fibonacci and Catalan Numbers

In a recent paper Aleksandar Cvetkovi c, Predrag Rajkovi c and Miloš Ivkovi c proved that for the Catalan numbers Cn the Hankel determinants of the sequence Cn þ Cnþ1 are Fibonacci numbers. Their proof depends on special properties of the corresponding orthogonal polynomials. In this paper we give a generalization of their result by other methods in order to give more insight into the situation...

APPROXIMATIONS OF STANDARD EQUIVALENCE RELATIONS AND BERNOULLI PERCOLATION AT pu

La notion de relation d’équivalence standard hyperfinie (i.e. réunion croissante de sous-relations standards finies) joue un rôle fondamental en théorie de l’équivalence orbitale. Plus généralement, on peut considérer la notion d’approximation d’une relation d’équivalence mesurée standardR, i.e. la possibilité d’écrireR comme réunion croissante d’une suite de sous-relations d’équivalence standa...