Where the monotone pattern (mostly) rules

Details Where the monotone pattern (mostly) rules Where the monotone pattern (mostly) rules

2007-04-11

arxiv.org/abs/0704.1489v1

Mathematics

Combinatorics

1 file 10 pages

Scientific paper

We consider pattern containment and avoidance with a very tight definition that was used first by Riordan more than 60 years ago. Using this definition, we prove the monotone pattern is easier to avoid than almost any other pattern of the same length. We also show that with this definition, almost all patterns of length $k$ are avoided by the same number of permutations of length $n$. The corresponding statements are not known to be true for more relaxed definitions of pattern containment. This is the first time we know of that expectations are used to compare numbers of permutations avoiding certain patterns.

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