Discrete Mathematics & Theoretical Computer Science |

- 1 Laboratoire Bordelais de Recherche en Informatique
- 2 The Mathematics Institute, Reyjavik University
- 3 Science Institute, University of Iceland
- 4 University of Iceland [Reykjavik]
- 5 Institute of Mathematics

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: HAL:hal-00396372v2

Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

Section: Proceedings

Published on: January 1, 2009

Imported on: January 31, 2017

Keywords: $(\mathrm{2+2})$-free poset,interval order,pattern-avoidance,enumeration,ascent sequence,kernel method,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
*Structures aléatoires discrètes et algorithmes*; Funder: French National Research Agency (ANR); Code: ANR-05-BLAN-0372

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