  We link $n$-jets of the affine monomial scheme defined by $x^p$ to the stable
set polytope of some perfect graph. We prove that, as $p$ varies, the dimension
of the coordinate ring of the scheme of $n$-jets as a $\mathbb{C}$-vector space
is a polynomial of degree $n+1,$ namely the Erhart polynomial of the stable set
polytope of that graph. One main ingredient for our proof is a result of Zobnin
who determined a differential Gr\"obner basis of the differential ideal
generated by $x^p.$ We generalize Zobnin's result to the bivariate case. We
study $(m,n)$-jets, a higher-dimensional analog of jets, and relate them to
regular unimodular triangulations of the $m\times n$-rectangle.
