A class of non-symmetric band determinants with the Gaussian q-binomial coefficients

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 formulæ 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.