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Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k. In this work we give two new algorithms for this well-studied problem, one whose running time is n^0.44k+o(k), and one whose running time is the better ofarXiv:1902.08809v2 fatcat:tb2kb2zh6zfavkjq4ez74jtjem