GCD matrices, posets, and nonintersecting paths

Abstract

We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature about GCD matrices and their relatives. Our main theorem is proved combinatorially using nonintersecting paths in a directed graph.Comment: 10 pages, see related papers at http://www.math.msu.edu/~saga