Solution of a research problem on trees of subsets
type: Item
instance of: scholarly article
title: Solution of a research problem on trees of subsets
zbMATH Open document ID: 0806.05006
DOI: 10.1007/BF02662068
author: Shiquan Wu
published in: Applied Mathematics. Series B (English Edition)
publication date: 1995-02-12T00:00:00Z
review text: Let \(X\) be an \(n\)-element set and \(\mathcal F\) a \(k\)-element collection of proper, non-empty subsets of \(X\) such that if \(A\), \(B\in {\mathcal F}\) then either \(A\subseteq B\), or \(B\subseteq A\), or they are disjoint. A closed formula is given for the number of those collections and it is shown that \(k\leq 2n-2\).
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 646767
zbMATH Keywords: trees of subsets
zbMATH Keywords: extremal set theory
zbMATH Keywords: enumeration
reviewed by: Péter Komjáth
MaRDI profile type: Publication
cites work: Q3741626
cites work: When is one estimate of evolutionary relationships a refinement of another?
cites work: The number of cladistic characters
cites work: Convergence properties of descent methods for unconstrained minization
full work available at URL: https://doi.org/10.1007/bf02662068
OpenAlex ID: W2323983998
description: scientific article; zbMATH DE number 646767