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{\bf William Y.C. Chen and Lewis H. Liu}
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{\bf Permutation Tableaux and  the Dashed Permutation Pattern 32--1}
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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.



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