q -Riordan array for q -Pascal matrix and its inverse matrix
| Autor: | Fatma Yesil, Dziemianczuk Maciej, Tuğlu Naim, E. Gokcen Kocer |
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| Přispěvatelé: | Amasya Üniversitesi, Tuglu, Naim -- 0000-0002-7277-0034, Dziemianczuk, Maciej -- 0000-0002-0553-7750, [Tuglu, Naim] Gazi Univ, Fac Sci, Dept Math, Ankara, Turkey -- [Yesil, Fatma] Amasya Univ, Fac Art & Sci, Dept Math, Amasya, Turkey -- [Dziemianczuk, Maciej] Univ Gdansk, Inst Informat, Gdansk, Poland -- [Kocer, E. Gokcen] Konya Necmettin Erbakan Univ, Fac Educ Meram, Konya, Turkey, Naim Tuğlu: 0000-0002-7277-0034, Maciej Dziemianczuk: 0000-0002-0553-7750, Necmettin Erbakan Üniversitesi Fen Fakültesi, Matematik ve Bilgisayar Bilimleri Bölümü Cebir ve Sayılar Teorisi Anabilim Dalı |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Matematik Hollow matrix Mathematics::Combinatorics General Mathematics Block matrix 010103 numerical & computational mathematics 0102 computer and information sciences Single-entry matrix Riordan representation Pascal matrices $q$-calculus 01 natural sciences Combinatorics Mathematics::Probability 010201 computation theory & mathematics Pascal matrices Matrix function Riordan representation Nonnegative matrix 0101 mathematics Involutory matrix q -calculus q-calculus Centrosymmetric matrix Pascal matrix Mathematics |
| Zdroj: | Volume: 40, Issue: 5 1038-1048 Turkish Journal of Mathematics |
| ISSN: | 1300-0098 1303-6149 |
| Popis: | 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. 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. |
| Databáze: | OpenAIRE |
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