On meet matrices on posets

DOI10.1016/0024-3795(95)00349-5zbMath0870.15016OpenAlexW2042814653MaRDI QIDQ2564902

Pentti Haukkanen

Publication date: 11 September 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00349-5

zbMATH Keywords

determinantsposetsinversegreatest common divisor matricesmeet matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Hermitian, skew-Hermitian, and related matrices (15B57) Matrices, determinants in number theory (11C20)

Related Items (26)

Lower bounds for determinants of matrices associated with classes of arithmetical Functions ⋮ Hyperdeterminants on meet-semilattices ⋮ Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions ⋮ Unnamed Item ⋮ Generalized eigenvalue problems for meet and join matrices on semilattices ⋮ Determinant and inverse of join matrices on two sets ⋮ The ancestral matrix of a rooted tree ⋮ Hyperdeterminants on semilattices ⋮ On meet and join matrices associated with incidence functions. ⋮ 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 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 ⋮ The parameterised complexity of counting connected subgraphs and graph motifs ⋮ Bounds for determinants of meet matrices associated with incidence functions ⋮ Explicit expressions of Smith's determinant on a poset ⋮ GCD matrices, posets, and nonintersecting paths ⋮ Power GCD Matrices for a UFD ⋮ Determinants of Matrices Associated with Incidence Functions on Posets ⋮ 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 ⋮ Some properties of row-adjusted meet and join matrices

Cites Work

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• The determinants of GCD matrices
• Greatest common divisor matrices
• On greatest common divisor matrices and their applications
• On GCD and LCM matrices
• Matrices associated with classes of arithmetical functions
• On Smith's determinant
• Another generalisation of smith's determinant
• Matrices associated with arithmetical functions
• Determinants on Semilattices
• Hadamard determinants Möbius functions, and the chromatic number of a graph
• Bivariate function algebras on Posets.

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