GCD matrices, posets, and nonintersecting paths
LINEAR & MULTILINEAR ALGEBRA, cilt.53, sa.2, ss.75-84, 2005 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 53 Sayı: 2
- Basım Tarihi: 2005
- Doi Numarası: 10.1080/03081080500054612
- Dergi Adı: LINEAR & MULTILINEAR ALGEBRA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.75-84
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Gazi Üniversitesi Adresli: Evet
Özet
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.