Kernelization lower bound for Permutation Pattern Matching

A permutation π contains a permutation σ as a pattern if it contains a subsequence of length |σ| whose elements are in the same relative order as in the permutation σ. This notion plays a major role in enumerative combinatorics. We prove that the problem does not have a polynomial kernel (under the widely believed complexity assumption NP 6⊆ co-NP/poly) by introducing a new polynomial reduction from the clique problem to permutation pattern matching.