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\vskip 1cm{\LARGE\bf 
Sums of Products of $s$-Fibonacci \\
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Polynomial Sequences
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{
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\large
Claudio de Jes\'{u}s Pita Ruiz Velasco \\
Universidad Panamericana\\
Mexico City, Mexico\\
\href{mailto:cpita@up.edu.mx}{\tt cpita@up.edu.mx} \\
}
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\begin{abstract}
We consider $s$-Fibonacci polynomial sequences $\left( F_{0}\left( x\right)
,F_{s}\left( x\right) ,F_{2s}\left( x\right) ,\ldots \right) $, where $s\in 
\mathbb{N}$ is given. By studying certain $z$-polynomials involving $s$%
-polyfibonomials $\binom{n}{k}_{\!F_{s}\left( x\right) }\!\!=\frac{%
F_{sn}\left( x\right) \cdots F_{s\left( n-k+1\right) }\left( x\right) }{%
F_{s}\left( x\right) \cdots F_{ks}\left( x\right) }$ and $s$-Gibonacci
polynomial sequences $\left( G_{0}\left( x\right) ,G_{s}\left( x\right)
,G_{2s}\left( x\right) ,\ldots \right) $, we generalize some known results
(and obtain some new results) concerning sums of products and addition
formulas of Fibonacci numbers.
\end{abstract}


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