NDLI: GCD matrices, posets, and nonintersecting paths

Content Provider	Scilit
Author	Altinisik, Ercan Sagan, Bruce E. Tuglu, Naim
Copyright Year	2005
Description	We show that with any finite partially ordered set P (which need not be a lattice) one can associate a matrix whose determinant factors nicely. This was also noted by D.A. Smith, although his proof uses manipulations in the incidence algebra of P while ours is combinatorial, using nonintersecting paths in a digraph. As corollaries, we obtain new proofs for and generalizations of a number of results in the literature about GCD matrices and their relatives.
Related Links	http://arxiv.org/pdf/math/0406155
Ending Page	84
Page Count	10
Starting Page	75
ISSN	03081087
e-ISSN	15635139
DOI	10.1080/03081080500054612
Journal	Linear and Multilinear Algebra
Issue Number	2
Volume Number	53
Language	English
Publisher	Informa UK Limited
Publisher Date	2005-03-01
Access Restriction	Open
Subject Keyword	Determinant Gcd Matrix Nonintersecting Paths 1991 Mathematics Subject Classifications: Primary 11c20 Secondary 05e99
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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GCD matrices, posets, and nonintersecting paths