Geodesic
$m$-partition boards and poly-Stirling numbers
Journal of integer sequences, Tome 13 (2010) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
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     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a0/}
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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/