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- W301555534 abstract "We present statistic-preserving bijections between four classes of combinatorial objects. Two of them, the class of unlabeled $(textrm{2+2})$-free posets and a certain class of chord diagrams (or involutions), already appeared in the literature, but were apparently not known to be equinumerous. The third one is a new class of pattern avoiding permutations, and the fourth one consists of certain integer sequences called $textit{ascent sequences}$. We also determine the generating function of these classes of objects, thus recovering a non-D-finite series obtained by Zagier for chord diagrams. Finally, we characterize the ascent sequences that correspond to permutations avoiding the barred pattern $3bar{1}52bar{4}$, and enumerate those permutations, thus settling a conjecture of Pudwell. Nous présentons des bijections, transportant de nombreuses statistiques, entre quatre classes d'objets. Deux d'entre elles, la classe des EPO (ensembles partiellement ordonnés) sans motif $(textrm{2+2})$ et une certaine classe d'involutions, sont déjà apparues dans la littérature. La troisième est une classe de permutations à motifs exclus, et la quatrième une classe de suites que nous appelons $textit{suites à montées}$. Nous déterminons ensuite la série génératrice de ces classes, retrouvant ainsi un résultat prouvé par Zagier pour les involutions sus-mentionnées. La série obtenue n'est pas D-finie. Apparemment, le fait qu'elle compte aussi les EPO sans motif $(textrm{2+2})$ est nouveau. Finalement, nous caractérisons les suites à montées qui correspondent aux permutations évitant le motif barré $3bar{1}52bar{4}$ et énumérons ces permutations, ce qui démontre une conjecture de Pudwell." @default.
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- W301555534 date "2009-01-01" @default.
- W301555534 modified "2023-09-25" @default.
- W301555534 title "Unlabeled $(2+2)$-free posets, ascent sequences and pattern avoiding permutations" @default.
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- W301555534 doi "https://doi.org/10.46298/dmtcs.2723" @default.
- W301555534 hasPublicationYear "2009" @default.
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