On meet and join matrices associated with incidence functions.
type: Item
instance of: scholarly article
title: On meet and join matrices associated with incidence functions.
zbMATH Open document ID: 1036.06005
DOI: 10.1016/S0024-3795(03)00497-X
author: Ismo Korkee
author: Pentti Haukkanen
published in: Linear Algebra and its Applications
publication date: 2003-10-15T00:00:00Z
review text: Let \(P\) be a finite lattice, let \(S=\{x_1,\dots,x_n\}\), and let \(f\) be a complex-valued function on \(P\). The authors give a broad study of the matrices \((S)_f=[f(x_i\wedge x_j)]_{i,j}\) and \([S]_f=[f(x_i\vee x_j)]_{i,j}\), obtain upper and lower bounds for their determinants, and apply the obtained results to the study of the GCD-matrices and LCM-matrices, occurring in elementary number theory. This approach permits to obtain in a uniform way several known results about these matrices, and also to obtain new information about them.
Mathematics Subject Classification ID: 06B99
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 1993123
zbMATH Keywords: finite lattices
zbMATH Keywords: GCD-matrix
zbMATH Keywords: LCM-matrix
zbMATH Keywords: meet matrix
zbMATH Keywords: join matrix
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
cites work: Q3050437
cites work: Q4101884
cites work: Q5841991
cites work: Matrices associated with arithmetical functions
cites work: Matrices associated with multiplicative functions
cites work: On meet matrices on posets
cites work: Some analogues of smith's determinant
cites work: On Smith's determinant
cites work: Bounds for determinants of matrices associated with classes of arithmetical functions
cites work: Bounds for determinants of meet matrices associated with incidence functions
cites work: Introduction to arithmetical functions
cites work: Semi-multiplicative functions
description: scientific article; zbMATH DE number 1993123