On meet and join matrices associated with incidence functions.
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Publication:1410716
DOI10.1016/S0024-3795(03)00497-XzbMath1036.06005MaRDI QIDQ1410716
Publication date: 15 October 2003
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Determinants, permanents, traces, other special matrix functions (15A15) Arithmetic functions; related numbers; inversion formulas (11A25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Lattices (06B99) Matrices, determinants in number theory (11C20)
Related Items (27)
Max and Min matrices with hyper-Fibonacci numbers ⋮ Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ Determinant and inverse of join matrices on two sets ⋮ Hyperdeterminants on semilattices ⋮ On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices ⋮ Studying the various properties of MIN and MAX matrices -- elementary vs. more advanced methods ⋮ Determinant and inverse of meet and join matrices ⋮ On the positive definiteness and eigenvalues of meet and join matrices ⋮ On a general form of meet matrices associated with incidence functions ⋮ On the eigenvalues of combined meet and join matrices ⋮ On eigenvalues of meet and join matrices associated with incidence functions ⋮ Smith meets Smith: Smith normal form of Smith matrix ⋮ On the divisibility of meet and join matrices ⋮ A proof of a conjecture on monotonic behavior of the smallest and the largest eigenvalues of a number theoretic matrix ⋮ An upper bound for the \(\ell_p\) norm of a gcd-related matrix ⋮ On unitary analogs of GCD reciprocal LCM matrices ⋮ GCD matrices, posets, and nonintersecting paths ⋮ ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES ⋮ Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs ⋮ Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets ⋮ On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture ⋮ Meet and join matrices in the poset of exponential divisors ⋮ On meet hypermatrices and their eigenvalues ⋮ A lattice-theoretic approach to the Bourque–Ligh conjecture ⋮ Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets ⋮ Some properties of row-adjusted meet and join matrices ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices
Cites Work
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- Introduction to arithmetical functions
- On Smith's determinant
- Matrices associated with multiplicative functions
- Bounds for determinants of matrices associated with classes of arithmetical functions
- Semi-multiplicative functions
- On meet matrices on posets
- Some analogues of smith's determinant
- Matrices associated with arithmetical functions
- Bounds for determinants of meet matrices associated with incidence functions
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