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


ARIKAN T., KILIÇ E.

QUAESTIONES MATHEMATICAE, vol.40, no.5, pp.645-660, 2017 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.2989/16073606.2017.1306596
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.645-660

Abstract

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.