  A ternary Permutation-CSP is specified by a subset $\Pi$ of the symmetric
group $\mathcal S_3$. An instance of such a problem consists of a set of
variables $V$ and a multiset of constraints, which are ordered triples of
distinct variables of $V.$ The objective is to find a linear ordering $\alpha$
of $V$ that maximizes the number of triples whose ordering (under $\alpha$)
follows a permutation in $\Pi$. We prove that all ternary Permutation-CSPs
parameterized above average have kernels with quadratic numbers of variables.
