منابع مشابه
Counting Connected Set Partitions of Graphs
Let G = (V,E) be a simple undirected graph with n vertices then a set partition π = {V1, . . . , Vk} of the vertex set of G is a connected set partition if each subgraph G[Vj ] induced by the blocks Vj of π is connected for 1 ≤ j ≤ k. Define qi(G) as the number of connected set partitions in G with i blocks. The partition polynomial is Q(G,x) = ∑n i=0 qi(G)x . This paper presents a splitting ap...
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The asymptotic behavior of the number of set partitions of an n-element set into blocks of distinct sizes is determined. This behavior is more complicated than is typical for set partition problems. Although there is a simple generating function, the usual analytic methods for estimating coefficients fail in the direct approach, and elementary approaches combined with some analytic methods are ...
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متن کاملRecords in Set Partitions
A partition of [n] = {1, 2, . . . , n} is a decomposition of [n] into nonempty subsets called blocks. We will make use of the canonical representation of a partition as a word over a finite alphabet, known as a restricted growth function. An element ai in such a word π is a strong (weak) record if ai > aj (ai > aj) for all j = 1, 2, . . . , i−1. Furthermore, the position of this record is i. We...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.07.001