ON A COMBINATION OF MEET AND JOIN MATRICES
Let be a subset of a lattice and let be a function. We present two structure theorems for the matrix where
and are appropriate real numbers. We also present formulae for the determinant and the inverse of on meet-closed sets S and join-closed sets S These formulae are generalizations of those obtained for meet matrices and join matrices in the literature. We also present our results in a number-theoretic setting, i.e., in the lattice where | is the usual divisibility relation.
meet matrix, join matrix, incidence function, GCD matrix, LCM matrix.