Correlation in partially ordered sets
type: Item
instance of: scholarly article
title: Correlation in partially ordered sets
zbMATH Open document ID: 0770.06001
DOI: 10.1016/0166-218X(92)90169-B
author: Peter Fishburn
published in: Discrete Applied Mathematics
publication date: 1993-01-17T00:00:00Z
review text: Basic results concerning correlation within ordered sets that focus on distributive lattices, systems of subsets ordered by proper inclusion and the family of linear extensions of an arbitrary finite ordered set are reviewed in this paper. Let us quote some interesting results: the Ahlswede-Daykin theorem, the FKG theorem, the universal correlation theorems of Winkler and Brightwell. Some theorems are proved carefully and the author mentions some open problems.
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 97212
zbMATH Keywords: FKG inequality
zbMATH Keywords: correlation
zbMATH Keywords: distributive lattices
zbMATH Keywords: systems of subsets ordered by proper inclusion
zbMATH Keywords: linear extensions
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
cites work: An inequality for the weights of two families of sets, their unions and intersections
cites work: Q5532570
cites work: Q3726125
cites work: Universal correlations in finite posets
cites work: Some correlation inequalities in finite posets
cites work: Linear extensions of infinite posets
cites work: A correlational inequality for linear extensions of a poset
cites work: Maximizing a correlational ratio for linear extensions of posets
cites work: Combinatorial Optimization Problems for Systems of Subsets
cites work: A note on linear extensions and incomparable pairs
cites work: The match of a random permutation has the FKG property
cites work: On the FKB conjecture for disjoint intersections
cites work: Correlation inequalities on some partially ordered sets
cites work: Q3952141
cites work: Q5184953
cites work: Some Monotonicity Properties of Partial Orders
cites work: Q5812325
cites work: Families of Non-disjoint subsets
cites work: A Monotonicity Property of Partial Orders
cites work: Association of probability measures on partially ordered spaces
cites work: Differences of Sets and A Problem of Graham
cites work: Note on the Ahlswede-Daykin inequality
cites work: On incomparable collections of sets
cites work: The FKG Inequality and Some Monotonicity Properties of Partial Orders
cites work: The XYZ conjecture and the FKG inequality
cites work: Q3815303
cites work: Q4871756
cites work: On a combinatorial conjecture concerning disjoint occurrences of events
cites work: Inequalities with applications to percolation and reliability
cites work: A Rearrangement Inequality and the Permutahedron
cites work: Correlation Among Partial Orders
full work available at URL: 0166-218x(92)90169-b
OpenAlex ID: W2033803833
Recommended article: Q3731641
Recommended article: On the correlation order
Recommended article: Q3626689
Recommended article: Q3362167
Recommended article: An Ordered Random Set Coupling
Recommended article: On correlations between complete sets
Recommended article: Q3498143
Recommended article: Q4246098
Recommended article: PARTIAL CORRELATIONS OF SEQUENCES AND THEIR APPLICATIONS
description: scientific article; zbMATH DE number 97212