GCD matrices, posets, and nonintersecting paths
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0406155,
title = {GCD matrices, posets, and nonintersecting paths},
author = {Ercan Altinisik and Bruce E. Sagan and Naim Tuglu},
journal= {arXiv preprint arXiv:math/0406155},
year = {2007}
}
Comments
10 pages, see related papers at http://www.math.msu.edu/~sagan