Geodesic
Generalized Stirling numbers and hyper-sums of powers of binomials coefficients
Claudio de J. Pita-Ruiz V.1
1Universidad Panamericana
The electronic journal of combinatorics, Tome 21 (2014) no. 1

Voir la notice de l'article provenant de la source The Electronic Journal of Combinatorics website

Zbl
We work with a generalization of Stirling numbers of the second kind related to the boson normal ordering problem (P. Blasiak et al.). We show that these numbers appear as part of the coefficients of expressions in which certain sequences of products of binomials, together with their partial sums, are written as linear combinations of some other binomials. We show that the number arrays formed by these coefficients can be seen as natural generalizations of Pascal and Lucas triangles, since many of the known properties on rows, columns, falling diagonals and rising diagonals in Pascal and Lucas triangles, are also valid (some natural generalizations of them) in the arrays considered in this work. We also show that certain closed formulas for hyper-sums of powers of binomial coefficients appear in a natural way in these arrays.
DOI : 10.37236/3787
Classification : 11B65, 05A10, 05A19, 11B73
Mots-clés : Stirling numbers, sums of powers of binomials coefficients

Claudio de J. Pita-Ruiz V.  1

1 Universidad Panamericana 
Claudio de J. Pita-Ruiz V. Generalized Stirling numbers and hyper-sums of powers of binomials coefficients. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3787
@article{10_37236_3787,
     author = {Claudio de J. Pita-Ruiz V.},
     title = {Generalized {Stirling} numbers and hyper-sums of powers of binomials coefficients},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {1},
     doi = {10.37236/3787},
     zbl = {1308.11020},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3787/}
}
TY  - JOUR
AU  - Claudio de J. Pita-Ruiz V.
TI  - Generalized Stirling numbers and hyper-sums of powers of binomials coefficients
JO  - The electronic journal of combinatorics
PY  - 2014
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/3787/
DO  - 10.37236/3787
ID  - 10_37236_3787
ER  - 
%0 Journal Article
%A Claudio de J. Pita-Ruiz V.
%T Generalized Stirling numbers and hyper-sums of powers of binomials coefficients
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3787/
%R 10.37236/3787
%F 10_37236_3787

Cité par Sources :