Skip to Main content Skip to Navigation
Conference papers

Computing generating functions of ordered partitions with the transfer-matrix method

Abstract : 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.
Complete list of metadata

Cited literature [8 references]  Display  Hide  Download

https://hal.inria.fr/hal-01184713
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 2:25:17 PM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:10:47 PM

File

dmAG0112.pdf
Publisher files allowed on an open archive

Identifiers

Citation

Masao Ishikawa, Anisse Kasraoui, Jiang Zeng. Computing generating functions of ordered partitions with the transfer-matrix method. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.193-202, ⟨10.46298/dmtcs.3508⟩. ⟨hal-01184713⟩

Share

Metrics

Record views

111

Files downloads

513