Notes on Hong's conjectures of real number power LCM matrices

DOI10.1016/j.jalgebra.2007.05.005zbMath1230.11036OpenAlexW2062171640WikidataQ122983946 ScholiaQ122983946MaRDI QIDQ2459990

Mao Li

Publication date: 9 November 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.05.005

zbMATH Keywords

nonsingularitygcd-closed setgreatest-type divisorlcm-closed setreal number power LCM matrixreciprocal real number power GCD matrix

Mathematics Subject Classification ID

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

Related Items (19)

Divisibility among determinants of power matrices associated with integer-valued arithmetic functions ⋮ 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 ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ 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 ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Studying the inertias of LCM matrices and revisiting the Bourque-Ligh conjecture ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ 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

Cites Work

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• Matrices associated with arithmetical functions
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• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES

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