Permutation Pattern Matching can be solved in n^{k/4+o(k)} time and in O(1.6181^n) polynomial-space time, with matching counting algorithms and an ETH-based near-optimal lower bound for the counting problem.
Hardness of permutation pattern matching
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Finding and counting permutations via CSPs
Permutation Pattern Matching can be solved in n^{k/4+o(k)} time and in O(1.6181^n) polynomial-space time, with matching counting algorithms and an ETH-based near-optimal lower bound for the counting problem.