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Discrete Mathematics & Theoretical Computer Science |
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 $3\bar{1}52\bar{4}$, and enumerate those permutations, thus settling a conjecture of Pudwell.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0510676 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.aam.2005.12.006 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0510676
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