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Abstract: We consider pattern containment and avoidance with a very tight definitionthat 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 patternof the same length.We also show that with this definition, almost all patterns of length $k$ areavoided by the same number of permutations of length $n$. The correspondingstatements are not known to be true for more relaxed definitions of patterncontainment. This is the first time we know of that expectations are used tocompare numbers of permutations avoiding certain patterns.

Author: Miklos Bona

Source: https://arxiv.org/


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