Sorting and preimages of pattern classes

نویسندگان

  • Anders Claesson
  • Henning Úlfarsson
چکیده

We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack, in terms of patterns. We also solve the long-standing problem of describing West-3-stack-sortable permutations. This requires a new type of generalized permutation pattern we call a decorated pattern. Résumé. On introduit un algorithme qui détermine quand un opérateur de tri (tels que le tri par une pile, ou le tri-bulle) produit un motif donné en sortie. Cet algorithme fournit une nouvelle preuve de la caractérisation des permutations 2-triables au sens de West (c’est-à-dire des permutations qui sont triées complètement par deux passages dans une pile) par des motifs interdits. On résout aussi le problème longtemps ouvert de la caractérisation des permutations 3-triables au sens de West. Ceci demande de définir un nouveau type de motifs généralisés, appelé motif décoré.

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عنوان ژورنال:
  • CoRR

دوره abs/1203.2437  شماره 

صفحات  -

تاریخ انتشار 2012