Computing generating functions of ordered partitions with the transfer-matrix method
نویسندگان
چکیده
An ordered partition of [n] := {1, 2, . . . , 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 Steingrı́msson, 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.
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Euler-mahonian Statistics on Ordered Partitions
An ordered partition with k blocks of [n] := {1, 2, . . . , n} is a sequence of k disjoint and nonempty subsets, called blocks, whose union is [n]. Clearly the number of such ordered partitions is k!S(n, k), where S(n, k) is the Stirling number of the second kind. A statistic on ordered partitions of [n] with k blocks is called Euler-Mahonian statistics if its generating polynomial is [k]q!Sq(n...
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