GCD matrices, posets, and nonintersecting paths

Details GCD matrices, posets, and nonintersecting paths GCD matrices, posets, and nonintersecting paths

2004-06-08

arxiv.org/abs/math/0406155v1

Mathematics

Combinatorics

10 pages, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

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.

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