The cyclic groups via the Pascal matrices and the generalized Pascal matrices

DEVECİ Ö., KARADUMAN E.

LINEAR ALGEBRA AND ITS APPLICATIONS, cilt.437, sa.10, ss.2538-2545, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 437 Sayı: 10
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.laa.2012.06.024
  • Dergi Adı: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2538-2545
  • Anahtar Kelimeler: Cyclic group, Multiplicative order, Pascal matrix
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, given a positive integer m, we consider the multiplicative order of upper and lower triangular matrices and symmetric matrices derived from Pascal's triangle when read modulo m. We also consider the corresponding problems when the binomial coefficients, ((j)(j)), are replaced by x(i-j)((j)(j)) and x(i+j)((j)(j)), where x is an integer satisfying certain divisibility hypotheses. We also offer some open conjectures on these orders. (C) 2012 Elsevier Inc. All rights reserved.