Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets

DOI10.1016/j.disc.2008.06.014zbMath1263.11042OpenAlexW1980749794MaRDI QIDQ1043604

Jianrong Zhao, Weiduan Feng, Shao-Fang Hong

Publication date: 9 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2008.06.014

zbMATH Keywords

divisibilityGCD matrixLCM matrixgcd-closed setgreatest-type divisor

Mathematics Subject Classification ID

Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (17)

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 classes of arithmetic functions ⋮ Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains ⋮ On the divisibility among power GCD and power LCM matrices on gcd-closed sets ⋮ 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 ⋮ Divisibility of matrices associated with multiplicative functions ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains ⋮ Divisibility of LCM matrices by totally nonnegative GCD matrices ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ GCD-closed sets and divisibility of Smith matrices ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices ⋮ ON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS

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