On a general form of join matrices associated with incidence functions

• Autores: Ismo Korkee, Pentti Haukkanen
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 75, Nº. 1-2, 2008, págs. 29-42
• Idioma: inglés
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• Resumen

  • Let be a join-semilattice with finite principal order filters and let denote the function on P × P defined by where f and g are incidence functions of P and h is a complex-valued function on P. We calculate the determinant and the inverse of the matrix , where S = {x 1, x 2,...,x n } is a join-closed subset of P and (x i , x j ?S, x i = x j = z) ? f(x i , z) = f(x j , z) holds for all z ? P. As special cases we obtain formulae for join matrices . The determinant formulae obtained for join matrices are known in the literature, whereas the inverse formulae are new. We also obtain new results for LCM and LCUM matrices, which are number-theoretic special cases of join matrices.