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On meet and join matrices associated with incidence functions

✍ Scribed by Ismo Korkee; Pentti Haukkanen

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 208 KB
Volume: 372
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00497-x

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✦ Synopsis

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 matrices on join-closed sets, bounds for the determinant of join matrices on all sets and a formula for the inverse of join matrices on join-closed sets are given. The concept of a semi-multiplicative function gives us formulae for meet matrices on join-closed sets and join matrices on meet-closed sets. Finally, we show what new the study of meet and join matrices contributes to the usual GCD and LCM matrices.

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