gaussian polynomials
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2021 ◽  
Vol 21 (1) ◽  
pp. 125-144
Author(s):  
NABIHA SABA ◽  
ALI BOUSSAYOUD ◽  
MOHAMED KERADA

In this study, we introduce a new class of generating functions of odd and even Gaussian (p,q)-Fibonacci numbers, Gaussian (p,q)-Lucas numbers, Gaussian (p,q)-Pell numbers, Gaussian (p,q)-Pell Lucas numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal Lucas numbers and we will recover the new generating functions of some Gaussian polynomials at odd and even terms. The technique used her is based on the theory of the so called symmetric functions.



10.37236/7820 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Dylan Pentland

Let $\left[{n \atop k}\right]_q$ be a $q$-binomial coefficient. Stanley conjectured that the function $f_{k,R}(n) = \left|\left\{\alpha : [q^{\alpha}] \left[{n \atop k}\right]_q  \equiv R \pmod{N}\right\}\right|$ is quasi-polynomial for $N$ prime. We prove this for any integer $N$ and obtain an expression for the generating function $F_{k,R}(x)$ for $f_{k,R}(n)$.



2019 ◽  
Vol 27 (3) ◽  
pp. 25-35
Author(s):  
Dorin Andrica ◽  
Ovidiu Bagdasar

AbstractWe deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of their extensions is applied.



Author(s):  
Angelica Castillo ◽  
Stephanie Flores ◽  
Anabel Hernandez ◽  
Brandt Kronholm ◽  
Acadia Larsen ◽  
...  
Keyword(s):  


2019 ◽  
Vol 23 (3-4) ◽  
pp. 589-611
Author(s):  
Angelica Castillo ◽  
Stephanie Flores ◽  
Anabel Hernandez ◽  
Brandt Kronholm ◽  
Acadia Larsen ◽  
...  
Keyword(s):  




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