A topological approach to divisibility of arithmetical functions and GCD matrices

DOI10.1080/03081087.2011.592141zbMath1276.11008OpenAlexW1965254700MaRDI QIDQ2879657

Publication date: 29 March 2012

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2011.592141

zbMATH Keywords

multiplicative functions GCD matrices topology on preposets

Mathematics Subject Classification ID

Partial orders, general (06A06) Arithmetic functions; related numbers; inversion formulas (11A25) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (1)

Coset topologies on \(\mathbb{Z}\) and arithmetic applications

Cites Work

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Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains
On the divisibility of meet and join matrices
Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets
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Matrices associated with classes of arithmetical functions
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On Smith's determinant
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Matrices associated with multiplicative functions
Some characterizations of totients
On homotopy types of Alexandroff spaces
Divisibility properties of power GCD matrices and power LCM matrices
An upper bound for the \(\ell_p\) norm of a gcd-related matrix
Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
Notes on the divisibility of GCD and LCM matrices
Gcd-closed sets and determinants of matrices associated with arithmetical functions
Smith meets Smith: Smith normal form of Smith matrix
On Nonsingular Power LCM Matrices
Infinite divisibility of Smith matrices
On unitary analogs of GCD reciprocal LCM matrices
Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains
Power GCD Matrices for a UFD
On the divisibility of power LCM matrices by power GCD matrices
Left multiples and right divisors of integral matrices
GCD matrices, posets, and nonintersecting paths
Continuous Lattices and Domains
Notes on power LCM matrices
Factorization of matrices associated with classes of arithmetical functions
LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS
Divisibility properties of Smith matrices

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