GCD matrices, posets, and nonintersecting paths

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Altinisik E., Sagan B., TUĞLU N.

LINEAR & MULTILINEAR ALGEBRA, cilt.53, sa.2, ss.75-84, 2005 (SCI-Expanded) identifier identifier

  • 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
  • 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.