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Abstract.
Let 
be subsets of the finite set
with 
and 
for all 
, 
. The
(r1,...,rp)-Stirling number of the second kind,
introduced in this paper and denoted by
,
counts the number of partitions of the set 
into k
classes (or blocks) such that the elements in each
, 
, are in different classes (or blocks). Combinatorial and algebraic properties of these numbers are explored.
Keywords: The (r1,...,rp)-Stirling Numbers of the Second Kind; the (r1,...,rp)-Bell Polynomials; Recurrence Relations; Generating Functions
Received: 2011-12-18
Revised: 2012-04-01
Accepted: 2012-05-18
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
