Streaming permutation pattern matching needs Θ(k log n) bits for monotone patterns, about sqrt(n) bits for four length-3 patterns, and linear bits for all larger non-monotone patterns.
[BC18] Omri Ben-Eliezer and Cl´ ement L
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Permutation patterns in streams
Streaming permutation pattern matching needs Θ(k log n) bits for monotone patterns, about sqrt(n) bits for four length-3 patterns, and linear bits for all larger non-monotone patterns.