m-Partition Boards and Poly-Stirling Numbers
Brian K. Miceli
Department of Mathematics
One Trinity Place
San Antonio, TX 78212-7200
We define a generalization of the Stirling numbers of the first and
second kinds and develop a new rook theory model to give combinatorial
interpretations to these numbers. These rook-theoretic interpretations
are used to give a direct combinatorial proof that two associated
matrices are inverses of each other. We also give combinatorial
interpretations of the numbers in terms of certain collections of
permutations and in terms of certain collections of set partitions. In
addition, many other well-known identities involving Stirling numbers
are generalized using this new model.
Full version: pdf,
Received September 8 2009;
revised version received February 26 2010.
Published in Journal of Integer Sequences, February 26 2010.
Journal of Integer Sequences home page