On the density of languages representing finite set partitions.
On the power values of Stirling numbers
On the problem of uniqueness for the maximum Stirling number(s) of the second kind.
On the sum of digits of some sequences of integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
-adic analysis and Bell numbers of two variables. (Analyse -adique et nombres de Bell à deux variables.)
Partial Bell polynomials and inverse relations.
Partition statistics and -Bell numbers .
Poly-Bernoulli numbers
By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.
Polynomials of multipartitional type and inverse relations
Chou, Hsu and Shiue gave some applications of Faà di Bruno's formula to characterize inverse relations. Our aim is to develop some inverse relations connected to the multipartitional type polynomials involving to binomial type sequences.
-Bernstein polynomials associated with -Stirling numbers and Carlitz's -Bernoulli numbers.
Remodified Bessel functions via coincidences and near coincidences.
Some congruences concerning the Bell numbers.
Some congruences for the partial Bell polynomials.
Some identities on the -Genocchi polynomials of higher-order and -Stirling numbers by the fermionic -adic integral on .
Some partition problems related to the Stirling numbers of the second kind
Some recurrence relations for Cauchy numbers of the first kind.
Some results for generalized harmonic numbers.
Stirling distributions and Stirling numbers of the second kind. Computational problems in statistics
Sur les polynomes de Stirling
The Akiyama-Tanigawa algorithm for Bernoulli numbers.