Permutation tableaux and the dashed permutation pattern 32-1
The electronic journal of combinatorics, Tome 18 (2011) no. 1
We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length $n$ and the number of occurrences of the dashed pattern 32–1 in permutations on $[n]$. We introduce the inversion number of a permutation tableau. For a permutation tableau $T$ and the permutation $\pi$ obtained from $T$ by the bijection of Corteel and Nadeau, we show that the inversion number of $T$ equals the number of occurrences of the dashed pattern 32–1 in the reverse complement of $\pi$. We also show that permutation tableaux without inversions coincide with L-Bell tableaux introduced by Corteel and Nadeau.
@article{10_37236_598,
author = {William Y.C. Chen and Lewis H. Liu},
title = {Permutation tableaux and the dashed permutation pattern 32-1},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/598},
zbl = {1233.05006},
url = {http://geodesic.mathdoc.fr/articles/10.37236/598/}
}
William Y.C. Chen; Lewis H. Liu. Permutation tableaux and the dashed permutation pattern 32-1. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/598
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