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      On some properties of permutation tableaux

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          Abstract

          We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the questions of Steingrimsson and Williams (math.CO/0507149), in particular, on the distribution of the bistatistic of numbers of rows and essential ones in permutation tableaux. We also consider and enumerate sets of permutation tableaux related to some pattern restrictions on permutations.

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          Restricted Dumont permutations, Dyck paths, and noncrossing partitions

          Toufik Mansour, Alexander Burstein, Sergi Elizalde (2006)
          We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding certain patterns of length 3 and 4 and give a natural bijection between 3142-avoiding Dumont permutations of the second kind and noncrossing partitions that uses cycle decomposition, as well as bijections between 132-, 231- and 321-avoiding Dumont permutations and Dyck paths. Finally, we enumerate Dumont permutations of the first kind simultaneously avoiding certain pairs of 4-letter patterns and another pattern of arbitrary length.
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            Publication date Created: 28 February 2007
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            ArXiV ID: math/0703004
            SO-VID: 94900a1c-67cc-49ff-ac9b-b23165542e41
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            ACM classes 05A05; 05A15; 05E10
            Comments 13 pages
            Categories math.CO

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