Labeled factorization of integers.
Lagrange inversion and Stirling number convolutions.
Linear recurrent sequences and powers of a square matrix.
Matchings in complete bipartite graphs and the -Lah numbers
We give a graph theoretic interpretation of -Lah numbers, namely, we show that the -Lah number counting the number of -partitions of an -element set into ordered blocks is just equal to the number of matchings consisting of edges in the complete bipartite graph with partite sets of cardinality and (, ). We present five independent proofs including a direct, bijective one. Finally, we close our work with a similar result for -Stirling numbers of the second kind.
Maximum Stirling numbers of the second kind.
Noch einmal die Stirlingschen Zahlen.
Nombres de Bell et somme de factorielles
Dj. Kurepa a conjecturé que pour tout nombre premier impair, , la somme n’est pas divisible par . Cette somme est reliée aux nombres de Bell qui apparaissent en combinatoire énumérative. Nous donnons une expression du -ième nombre de Bell modulo comme la trace de la puissance -ième d’un élément fixe dans l’extension d’Artin-Schreier de degré du corps premier à éléments. Cette expression permet de démontrer la conjecture de Kurepa en la ramenant à un problème d’algèbre linéaire.
Nouvelles propriétés arithmétiques des nombres de Bell
On 2-adic orders of Stirling numbers of the second kind.
On a class of combinatorial sums involving generalized factorials.
On a generalization of an approximation operator defined by A. Lupaş.
On a generalized recurrence for Bell numbers.
On a new family of generalized Stirling and Bell numbers.
On a relation between the Riemann zeta function and the Stirling numbers.
On generalizations of the Stirling number triangles.
On partitions, surjections, and Stirling numbers.
On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications
On -Euler numbers related to the modified -Bernstein polynomials.
On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
On the coefficients of the asymptotic expansion of .