%p33abs.tex k-Stirling numbers paper abstract
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\centerline{W. L a n g : ``On Generalizations of the Stirling Number 
Triangles''.}\par
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\centerline{\bf Abstract}
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Sequences of generalized {\sl Stirling} numbers of both kinds are presented.
These sequences of triangles of numbers (or infinite dimensional lower 
triangular matrices) will be denoted by $S2(k;n,m)$ and $S1(k;n,m)$, 
with $k\in \bf Z $. 
The original {\sl Stirling} number triangles of the second and first kind 
show up for $k=1$. $S2(2;n,m)$ is identical with
the unsigned S1(2;n,m) triangle, called $S1p(2;n,m)$, which represents the 
triangle of signless {\sl Lah} numbers. 
Associated number triangles, called $s2(k;n,m)$ and $s1(k;n,m)$, are also 
defined. $s2(2;n,m)$ as well as $s1(2;n+1,m+1)$ is {\sl Pascal'}s triangle, 
and $s2(-1,n,m)$ turns out to be {\sl Shapiro}'s {\sl Catalan} triangle.  
\par
Generating functions for the columns of these triangles
are given.  Each ${\bf S2}(k)$ and each ${\bf S1}(k)$ matrix is an example of a
{\sl Jabotinsky-}matrix. Therefore, the generating functions of the rows 
of these triangular arrays constitute exponential convolution polynomials.
The sequences of the row-sums of these triangles are also considered.\par
The connection to the problem of finding finite transformations
from infinitesimal ones generated by $x^k\,\Dx{}$, for $k\in \bf Z$, is 
made.
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