Enumerating nested and consecutive partitions
نویسندگان
چکیده
منابع مشابه
Enumerating Consecutive and Nested Partitions for Graphs
Consecutive and nested partitions have been extensively studied in the set-partition problem as tools with which to search efficiently for an optimal partition. We extend the study of consecutive and nested partitions on a set of integers to the vertex-set of a graph. A subset of vertices is considered consecutive if the subgraph induced by the subset is connected. In this sense the partition p...
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We consider the problem of partitioning the vertex-set of a tree to p parts to minimize a cost function. Since the number of partitions is exponential in the number of vertices, it is helpful to identify small classes of partitions which also contain optimal partitions. Two such classes, called consecutive partitions and nested partitions, have been well studied for the set partition problem, w...
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Let P (n, k) denote the set of partitions of [n] = {1, 2, . . . , n} containing exactly k blocks. Given a partition Π = B1/B2/ · · · /Bk ∈ P (n, k) in which the blocks are listed in increasing order of their least elements, let π = π1π2 · · · πn denote the canonical sequential form wherein j ∈ Bπj for all j ∈ [n]. In this paper, we supply an explicit formula for the generating function which co...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1995
ISSN: 0097-3165
DOI: 10.1016/0097-3165(95)90097-7