Statistics on ordered partitions of sets
نویسندگان
چکیده
منابع مشابه
STATISTICS ON ORDERED PARTITIONS OF SETS AND q-STIRLING NUMBERS
An ordered partition of [n] := {1, 2, . . . , n} is a sequence of its disjoint subsets whose union is [n]. The number of ordered partitions of [n] with k blocks is k!S(n, k), where S(n, k) is the Stirling number of second kind. In this paper we prove some refinements of this formula by showing that the generating function of some statistics on the set of ordered partitions of [n] with k blocks ...
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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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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]. In this article, we consider Steingŕımsson’s conjectures about Euler-Mahonian statistics on ordered partitions dated back to 1997. We encode ordered partitions by walks in some digraphs and then derive their generating functions using the transfer-m...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2020
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2020.v11.n3.a8