$q$-Riordan array for $q$-Pascal matrix and its inverse matrix | Zendy

Naim Tuğlu | Zendy; Fatma YEŞİL | Zendy; Maciej Dziemiańczuk | Zendy; E. Gökçen Koçer | Zendy

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$q$-Riordan array for $q$-Pascal matrix and its inverse matrix

Author(s) -

Naim Tuğlu,

Fatma YEŞİL,

Maciej Dziemiańczuk,

E. Gökçen Koçer

Publication year - 2016

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1506-56

Subject(s) - mathematics , pascal (unit) , inverse , companion matrix , pascal matrix , matrix (chemical analysis) , binary number , r matrix , representation (politics) , algebra over a field , pure mathematics , combinatorics , symmetric matrix , mathematical analysis , nonnegative matrix , arithmetic , geometry , physics , eigenvalues and eigenvectors , polynomial matrix , matrix polynomial , materials science , polynomial , composite material , quantum mechanics , law , political science , atomic physics , politics

In this paper, we prove the q -analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations ∗q and ∗1/q , we obtain a q -analogue of the Riordan representation of the q -Pascal matrix. In addition, by aid of the q -Lagrange expansion formula we get q -Riordan representation for its inverse matrix.

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