Notes on the divisibility of GCD and LCM matrices.
Haukkanen, Pentti, Korkee, Ismo (2005)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “Determinant and inverse of meet and join matrices.”
Notes on the divisibility of GCD and LCM matrices.
A Pfaffian-Hafnian analogue of Borchardt's identity.
Ishikawa, Masao, Kawamuko, Hiroyuki, Okada, Soichi (2005)
The Electronic Journal of Combinatorics [electronic only]
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Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
Siao Hong, Shuangnian Hu, Shaofang Hong (2016)
Open Mathematics
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Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of...
An analysis of GCD and LCM matrices via the -factorization.
Ovall, Jeffrey S. (2004)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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On Zeilberger's constant term for Andrew's TSSCPP theorem.
Xin, Guoce (2011)
The Electronic Journal of Combinatorics [electronic only]
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Determinants of matrices associated with incidence functions on posets
Shaofang Hong, Qi Sun (2004)
Czechoslovak Mathematical Journal
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Let be a finite subset of a partially ordered set . Let be an incidence function of . Let denote the matrix having evaluated at the meet of and as its -entry and denote the matrix having evaluated at the join of and as its -entry. The set is said to be meet-closed if for all . In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set . We also obtain necessary and sufficient conditions for...
Some factorizations of matrix functions in several variables
Jaromír Šimša (1992)
Archivum Mathematicum
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We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.