On the Bourque-Ligh conjecture of least common multiple matrices

From MaRDI portal
Publication:1305037

DOI10.1006/jabr.1998.7844zbMath1015.11007OpenAlexW2044636635WikidataQ123092194 ScholiaQ123092194MaRDI QIDQ1305037

Shao-Fang Hong

Publication date: 19 November 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7844




Related Items (40)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functionsDeterminants of Smith matrices on three coprime divisor chains and divisibilityASYMPTOTIC BEHAVIOR OF THE SMALLEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (mod r)On a certain determinant for a U.F.D.On the factorization of LCM matrices on gcd-closed setsDivisibility among power matrices associated with classes of arithmetic functionsHyperdeterminants on meet-semilatticesDivisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chainsLU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONSOn the divisibility among power GCD and power LCM matrices on gcd-closed setsDivisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chainsDivisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chainsUpper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral normASYMPTOTIC BEHAVIOR OF LARGEST EIGENVALUE OF MATRICES ASSOCIATED WITH COMPLETELY EVEN FUNCTIONS (MOD r)THERE DOES NOT EXIST AN ODD SINGULAR NUMBER OF THE FORM plqrDivisibility of matrices associated with multiplicative functionsOn the positive definiteness and eigenvalues of meet and join matricesDeterminants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chainsNotes on Hong's conjectures of real number power LCM matricesStudying the singularity of LCM-type matrices via semilattice structures and their Möbius functionsDivisibility properties of power GCD matrices and power LCM matricesDivisibility among power GCD matrices and among power LCM matrices on two coprime divisor chainsNonsingularity of matrices associated with classes of arithmetical functions on lcm-closed setsASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICESPower GCD Matrices for a UFDNon-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed setsOn inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjectureDeterminants of Matrices Associated with Incidence Functions on PosetsOn the divisibility of power LCM matrices by power GCD matricesOn Hong’s conjecture for power LCM matricesStudying the inertias of LCM matrices and revisiting the Bourque-Ligh conjectureDivisibility among power GCD matrices and among power LCM matrices on three coprime divisor chainsGCD-closed sets and divisibility of Smith matricesA lattice-theoretic approach to the Bourque–Ligh conjectureDivisibility of power LCM matrices by power GCD matrices on gcd-closed setsDivisibility properties of power LCM matrices by power GCD matrices on gcd-closed setsNonsingularity of least common multiple matrices on gcd-closed setsOn Nonsingular Power LCM MatricesA topological approach to divisibility of arithmetical functions and GCD matricesON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS



Cites Work


This page was built for publication: On the Bourque-Ligh conjecture of least common multiple matrices