A CLASS OF NON-SYMMETRIC BAND DETERMINANTS WITH THE GAUSSIAN q-BINOMIAL COEFFICIENTS


ARIKAN T. , KILIÇ E.

QUAESTIONES MATHEMATICAE, cilt.40, ss.645-660, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 40 Konu: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.2989/16073606.2017.1306596
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Sayfa Sayıları: ss.645-660

Özet

A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper bandwith is s and lower bandwith is r. We give explicit formula for the determinant, the inverse (along with its infinity-norm when q -> 1) and the LU-decomposition of the class. We use the celebrated q-Zeilberger algorithm and unimodality property to prove claimed results.