منابع مشابه
A Sperner-Type Theorem for Set-Partition Systems
A Sperner partition system is a system of set partitions such that any two set partitions P and Q in the system have the property that for all classes A of P and all classes B of Q, A 6⊆ B and B 6⊆ A. A k-partition is a set partition with k classes and a k-partition is said to be uniform if every class has the same cardinality c = n/k. In this paper, we prove a higher order generalization of Sp...
متن کاملThe Sperner Property for Integer Partition Posets
We examine the integer partition poset, Pn, ordered by a covering relation to determine whether or not it has the Sperner property. To show that Pn is Sperner we must prove it satisfies unimodality and the bipartite matching property. It has been shown computationally by Canfield for n ≤ 2000 and asymptotically by Szekeres for n sufficiently large that Pn is unimodal. Computationally, we have i...
متن کاملOn Saturated k-Sperner Systems
Given a set X, a collection F ⊆ P(X) is said to be k-Sperner if it does not contain a chain of length k + 1 under set inclusion and it is saturated if it is maximal with respect to this property. Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi and Patkós conjectured that, if |X| is sufficiently large with respect to k, then the minimum size of a saturated k-Sperner system F ⊆ P(X) is 2k−1. In this ...
متن کاملShattering-extremal set systems from Sperner families
We say that a set system F ⊆ 2 shatters a given set S ⊆ [n] if 2 = {F ∩ S : F ∈ F}. The Sauer-Shelah lemma states that in general, a set system F shatters at least |F| sets. Here we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly |F| sets. A conjecture of Rónyai and the second author and of Litman and Moran states that if a family is shatte...
متن کاملA partition-based algorithm for clustering large-scale software systems
Clustering techniques are used to extract the structure of software for understanding, maintaining, and refactoring. In the literature, most of the proposed approaches for software clustering are divided into hierarchical algorithms and search-based techniques. In the former, clustering is a process of merging (splitting) similar (non-similar) clusters. These techniques suffered from the drawba...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Designs
سال: 2012
ISSN: 1063-8539
DOI: 10.1002/jcd.21330