On cross-intersecting families of set partitions
type: Item
instance of: scholarly article
title: On cross-intersecting families of set partitions
zbMATH Open document ID: 1267.05035
author: Cheng Yeaw Ku
author: K. B. Wong
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v19i4p49
review text: Summary: Let \(\mathcal{B}(n)\) denote the collection of all set partitions of \([n]\). Suppose \({\mathcal{A}}_1,{\mathcal{A}}_2 \subseteq \mathcal{B}(n)\) are cross-intersecting, i.e., for all \(A_1 \in {\mathcal{A}}_1\) and \(A_2 \in {\mathcal{A}}_2\), we have \(A_1 \cap A_2 \neq \varnothing\). It is proved that for sufficiently large \(n\), \(|{\mathcal{A}}_1| |{\mathcal{A}}_2| \leq B_{n-1}^2 \) where \(B_{n}\) is the \(n\)-th Bell number. Moreover, equality holds if and only if \({\mathcal{A}}_1 = {\mathcal{A}}_2\) and \({\mathcal{A}}_1\) consists of all set partitions with a fixed singleton.
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 6171832
zbMATH Keywords: cross-intersecting
zbMATH Keywords: Erdős-Ko-Rado
zbMATH Keywords: set-partitions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171832