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Determinants of Matrices Associated with Incidence Functions on Posets

โœ Scribed by Shaofang Hong; Qi Sun

Book ID
111577434
Publisher
Springer
Year
2004
Tongue
English
Weight
160 KB
Volume
54
Category
Article
ISSN
0011-4642

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๐Ÿ“œ SIMILAR VOLUMES

On meet and join matrices associated wit
On meet and join matrices associated with incidence functions
โœ Ismo Korkee; Pentti Haukkanen ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 208 KB

We study recently meet matrices on meet-semilattices as an abstract generalization of greatest common divisor (GCD) matrices. Analogously, in this paper we consider join matrices on lattices as an abstract generalization of least common multiple (LCM) matrices. A formula for the determinant of join

On eigenvalues of meet and join matrices
On eigenvalues of meet and join matrices associated with incidence functions
โœ Pauliina Ilmonen; Pentti Haukkanen; Jorma K. Merikoski ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 166 KB

Let (P , , โˆง) be a locally finite meet semilattice. Let S = {x 1 , x 2 , . . . , x n }, x i x j โ‡’ i j, be a finite subset of P and let f be a complex-valued function on P . Then the n ร— n matrix (S) f , where is called the meet matrix on S with respect to f . The join matrix on S with respect to f