A ternary permutation-csp is specified by a subset p of the symmetric group s3. 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 a of v that maximizes the number of triples whose rearrangement (under a) follows a permutation in p. We prove that every ternary permutation-csp parameterized above average has a kernel with a quadratic number of variables.
Gutin, G., van Iersel, L., Mnich, M., & Yeo, A. (2012). Every ternary permutation constraint satisfaction problem parameterized above average has a kernel with a quadratic number of variables. Journal of Computer and System Sciences, 78(1), 151-163. https://doi.org/10.1016/j.jcss.2011.01.004