Geodesic
\(m\)-partition boards and poly-Stirling numbers
Journal of integer sequences, Tome 13 (2010) no. 3
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.
Classification : 05A15, 05E05
Keywords: rook theory, rook placement, Stirling numbers, inverses 
@article{JIS_2010__13_3_a0,
     author = {Miceli,  Brian K.},
     title = {\(m\)-partition boards and {poly-Stirling} numbers},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {3},
     zbl = {1228.05037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a0/}
}
TY  - JOUR
AU  - Miceli,  Brian K.
TI  - \(m\)-partition boards and poly-Stirling numbers
JO  - Journal of integer sequences
PY  - 2010
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a0/
LA  - en
ID  - JIS_2010__13_3_a0
ER  - 
%0 Journal Article
%A Miceli,  Brian K.
%T \(m\)-partition boards and poly-Stirling numbers
%J Journal of integer sequences
%D 2010
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a0/
%G en
%F JIS_2010__13_3_a0
Miceli,  Brian K. \(m\)-partition boards and poly-Stirling numbers. Journal of integer sequences, Tome 13 (2010) no. 3. http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a0/