A class of non-symmetric band determinants with the Gaussian q-binomial coefficients. Issue 5 (29th August 2017)

• Record Type: Journal Article
• Authors: Arikan, Talha; Kiliç, Emrah
• Is Part Of: Quaestiones mathematicae. Volume 40:Issue 5(2017)
• Page Start: 645
• Page End: 660
• Publication Date: 2017-08-29
• Subjects: 15B36 -- 15A15 -- 15A23 -- 11B65 -- 05A10; Determinant -- inverse matrix -- LU -decomposition -- Gaussian q-binomial coefficients -- Fibonomial coefficients -- Zeilberger's algorithm -- unimodality; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2017.1306596
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: A class of symmetric band matrices of bandwidth 2 r +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.