The number of bar{3}bar{1}542-avoiding permutations
Combinatorics
2011-12-30 v3
Abstract
We confirm a conjecture of Lara Pudwell and show that permutations of [n] that avoid the barred pattern bar{3}bar{1}542 are counted by OEIS sequence A047970. In fact, we show bijectively that the number of bar{3}bar{1}542 avoiders of length n with j+k left-to-right maxima, of which j initiate a descent in the permutation and k do not, is {n}-choose-{k} j! StirlingPartition{n-j-k}{j}, where StirlingPartition{n}{j} is the Stirling partition number.
Cite
@article{arxiv.1111.3088,
title = {The number of bar{3}bar{1}542-avoiding permutations},
author = {David Callan},
journal= {arXiv preprint arXiv:1111.3088},
year = {2011}
}
Comments
5 pages, 2 figures, minor corrections