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GCD matrices, posets, and nonintersecting paths

2004/06/08 by Ercan Altinisik, Altinisik, Ercan, Bruce E. Sagan +3
Mathematics · #11A25 #11C20 (Primary) 05E99 #15A36 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E99 #msc:11A25 #msc:11C20 #msc:15A36

paper · pdf · doi:10.48550/arxiv.math/0406155

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

arxiv created 2004/06/08 · arxiv updated 2009/12/01

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.

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