Geodesic
Computing generating functions of ordered partitions with the transfer-matrix method
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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An ordered partition of $[n]:=\{1,2,\ldots, n\}$ is a sequence of disjoint and nonempty subsets, called blocks, whose union is $[n]$. The aim of this paper is to compute some generating functions of ordered partitions by the transfer-matrix method. In particular, we prove several conjectures of Steingrímsson, which assert that the generating function of some statistics of ordered partitions give rise to a natural $q$-analogue of $k!S(n,k)$, where $S(n,k)$ is the Stirling number of the second kind. 
@article{DMTCS_2006_special_252_a32,
     author = {Ishikawa, Masao and Kasraoui, Anisse and Zeng, Jiang},
     title = {Computing generating functions of ordered partitions with the transfer-matrix method},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3508},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3508/}
}
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Ishikawa, Masao; Kasraoui, Anisse; Zeng, Jiang. Computing generating functions of ordered partitions with the transfer-matrix method. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3508. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3508/

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