Superpatterns and Generalizations of Layered Permutations

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In the study of permutation patterns, superpatterns are permutations that contain many patterns at least once. For a set P of permutations, we say that a permutation σ is a P -superpattern if it contains every permutation in P , and we denote by sp(P ) the shortest length of all P -superpatterns. When P is the set of layered permutations of length k, it has been shown that sp(P ) = Θ(k log(k)). The notion of superpatterns can be extended naturally to words. In this talk, we explore some generalizations of layered permutations to ‘layered words’ and seek to find shortest lengths for superpatterns containing these sets.


Midwestern Conference on Combinatorics and Combinatorial Computing (MCCCC)


Charleston, SC