(a, B)-rectangle Patterns in Permutations and Words

@article{Kitaev2015aBP,
  title={(a, B)-rectangle Patterns in Permutations and Words},
  author={S. Kitaev and J. Remmel},
  journal={Discret. Appl. Math.},
  year={2015},
  volume={186},
  pages={128-146}
}
In this paper, we introduce the notion of an ( a , b ) -rectangle pattern on permutations which is closely related to the notion of successive elements (bonds) in permutations and to mesh patterns introduced recently by Branden and Claesson. We call the ( k , k ) -rectangle pattern the k -box pattern. We show that we can derive an explicit formula for the number of permutations of S n which have the maximum possible occurrences of the 1-box pattern by using a new enumerative result on pattern… Expand
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