Determinant and Inverse of Meet and Join Matrices

Abstract

We define meet and join matrices on two subsetsXandYof a lattice(P,≼)with respect to a complex-valued functionfonPby(X,Y)f=(f(xi∧yi))and[X,Y]f=(f(xi∨yi)), respectively. We present expressions for the determinant and the inverse of(X,Y)fand[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)fand[S]f.