Permutation Tableaux and the Dashed Permutation Pattern 32–1
William Y.C. Chen and Lewis H. Liu
Abstract: 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 π 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 π. We also show that permutation tableaux without inversions coincide with L-Bell tableaux introduced by Corteel and Nadeau.
AMS Classification: 05A05, 05A19
Keywords: Permutation tableaux, dashed permutation patten.