International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 37580, 11 pages
Research Article

Determinant and Inverse of Meet and Join Matrices

Ercan Altinisik,1 Naim Tuglu,1 and Pentti Haukkanen2

1Department of Mathematics, Faculty of Arts and Sciences, Gazi University, Teknikokullar 06500, Ankara, Turkey
2Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, Finland

Received 2 March 2007; Accepted 18 April 2007

Academic Editor: Dihua Jiang

Copyright © 2007 Ercan Altinisik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We define meet and join matrices on two subsets X and Y of a lattice (P,) with respect to a complex-valued function f on P by (X,Y)f=(f(xiyi)) and [X,Y]f=(f(xiyi)), respectively. We present expressions for the determinant and the inverse of (X,Y)f and [X,Y]f, and as special cases we obtain several new and known formulas for the determinant and the inverse of the usual meet and join matrices (S)f and [S]f.