Three Generalizations of Davenport-Schinzel Sequences
Abstract
We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-s double DS sequences, for all s, sharp bounds on sequences avoiding catenated permutations (aka formation free sequences), and new lower bounds on sequences avoiding zig-zagging patterns.
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