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#### On Fibonomial sums identities with special sign functions: analytically q-calculus approach

(De Gruyter Open Ltd, 2018-06-26)

Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809-818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. ...

#### Evaluation of sums involving products of Gaussian q-binomial coefficients with applications to Fibonomial sums

(Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2017)

Sums of products of two Gaussian q-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting ...

#### Closed form evaluation of restricted sums containing squares of Fibonomial coefficients

(Politechnica University of Bucharest, 2016)

We give a systematic approach to compute certain sums of squares Fibonomial coefficients with powers of generalized Fibonacci and Lucas numbers as coefficients; the range of the summation is not the natural one but about ...

#### A class of non-symmetric band determinants with the Gaussian q-binomialcoefficients

(Taylor and Francis Ltd., 2017)

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 ...

#### Evaluation of sums containing triple aerated generalized Fibonomial coefficients

(De Gruyter Open Ltd, 2017-04)

We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ...

#### Formulæ related to the q-Dixon formula with applications to Fibonomial sums

(Kluwer Academic Publishers, 2015-06)

The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...

#### A proof of a conjecture of Marques and Trojovsky

(University of Miskolc, 2014)

In this paper, we consider Marques and Trojovsky's conjecture involving Fibonomial coefficients, Fibonacci and Lucas numbers. After rewriting it in terms of Gaussian q-binomial coefficients and q-Pochhammer symbols, we ...

#### Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions

(World Scientific Publishing Co. Pte Ltd, 2016-03)

We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ...