  Lucas polynomials are polynomials in $s_1$ and $s_2$ defined recursively by
$\{0\}=0$, $\{1\}=1$, and $\{m\}=s_1\{m-1\}+s_2\{m-2\}$ for $m \geq 2$. We
generalize Lucas polynomials from 2-variable polynomials to multivariable
polynomials. This is done by first defining $r$-Lucas polynomials $\{m\}_r$ in
the variables $s_1$, $s_r$, and $s_{2r}$. We show that the binomial analogues
of the $r$-Lucas polynomials are polynomial and give a combinatorial
interpretation for them. We then extend the generalization of Lucas polynomials
to an arbitrarily large set of variables. Recursively defined generating
functions are given for these multivariable Lucas polynomials. We conclude by
giving additional applications and insights.
