Nonsingularity of least common multiple matrices on gcd-closed sets

DOI10.1016/j.jnt.2005.03.004zbMath1080.11022OpenAlexW1993888825MaRDI QIDQ2566161

Shao-Fang Hong

Publication date: 22 September 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.03.004

zbMATH Keywords

Smith's determinantnonsingularityGCD matrixLCM matrixBourque-Ligh conjecture

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (25)

Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ ASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r) ⋮ Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains ⋮ Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains ⋮ ASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r) ⋮ THERE DOES NOT EXIST AN ODD SINGULAR NUMBER OF THE FORM p^lqr ⋮ Divisibility of matrices associated with multiplicative functions ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ Notes on Hong's conjectures of real number power LCM matrices ⋮ Studying the singularity of LCM-type matrices via semilattice structures and their Möbius functions ⋮ Divisibility properties of power GCD matrices and power LCM matrices ⋮ Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains ⋮ Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Power GCD Matrices for a UFD ⋮ On the divisibility of power LCM matrices by power GCD matrices ⋮ On Hong’s conjecture for power LCM matrices ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ A lattice-theoretic approach to the Bourque–Ligh conjecture ⋮ Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ On Nonsingular Power LCM Matrices

Cites Work

• Unnamed Item
• On GCD and LCM matrices
• On LCM matrices on GCD-closed sets
• On the Bourque-Ligh conjecture of least common multiple matrices
• Matrices associated with classes of arithmetical functions
• Arithmetical properties of generalized Ramanujan sums
• Gcd-closed sets and determinants of matrices associated with arithmetical functions
• A Generalization of Smith's Determinant
• Another generalisation of smith's determinant
• Lower bounds for determinants of matrices associated with classes of arithmetical Functions

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