Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations

Mireille Bousquet-Melou, Anders Claesson, Mark Dukes, Sergey Kitaev

Research output: Contribution to conferencePaper

2 Citations (Scopus)

Abstract

We present statistic-preserving bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (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 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 31524, and enumerate those permutations, thus settling a conjecture of Pudwell.

Conference

Conference21st International Conference on Formal Power Series & Algebraic Combinatorics
CountryAustria
CityHagenberg
Period20/07/0924/07/09

Fingerprint

Pattern-avoiding Permutation
Ascent
Poset
Statistics
Chord Diagrams
Permutation
Integer Sequences
Bijection
Involution
Generating Function
Statistic
Class
Series

Keywords

  • (2+2)-free posets
  • interval order
  • pattern avoidance
  • ascent sequences
  • kernel method

Cite this

Bousquet-Melou, M., Claesson, A., Dukes, M., & Kitaev, S. (2009). Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations. 216-228. Paper presented at 21st International Conference on Formal Power Series & Algebraic Combinatorics, Hagenberg, Austria.
Bousquet-Melou, Mireille ; Claesson, Anders ; Dukes, Mark ; Kitaev, Sergey. / Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations. Paper presented at 21st International Conference on Formal Power Series & Algebraic Combinatorics, Hagenberg, Austria.13 p.
@conference{a0f8c7cca91b45da96433599d4c56342,
title = "Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations",
abstract = "We present statistic-preserving bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (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 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 31524, and enumerate those permutations, thus settling a conjecture of Pudwell.",
keywords = "(2+2)-free posets, interval order, pattern avoidance, ascent sequences, kernel method",
author = "Mireille Bousquet-Melou and Anders Claesson and Mark Dukes and Sergey Kitaev",
year = "2009",
language = "English",
pages = "216--228",
note = "21st International Conference on Formal Power Series & Algebraic Combinatorics ; Conference date: 20-07-2009 Through 24-07-2009",

}

Bousquet-Melou, M, Claesson, A, Dukes, M & Kitaev, S 2009, 'Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations' Paper presented at 21st International Conference on Formal Power Series & Algebraic Combinatorics, Hagenberg, Austria, 20/07/09 - 24/07/09, pp. 216-228.

Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations. / Bousquet-Melou, Mireille; Claesson, Anders; Dukes, Mark; Kitaev, Sergey.

2009. 216-228 Paper presented at 21st International Conference on Formal Power Series & Algebraic Combinatorics, Hagenberg, Austria.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations

AU - Bousquet-Melou, Mireille

AU - Claesson, Anders

AU - Dukes, Mark

AU - Kitaev, Sergey

PY - 2009

Y1 - 2009

N2 - We present statistic-preserving bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (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 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 31524, and enumerate those permutations, thus settling a conjecture of Pudwell.

AB - We present statistic-preserving bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (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 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 31524, and enumerate those permutations, thus settling a conjecture of Pudwell.

KW - (2+2)-free posets

KW - interval order

KW - pattern avoidance

KW - ascent sequences

KW - kernel method

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAK0118

M3 - Paper

SP - 216

EP - 228

ER -

Bousquet-Melou M, Claesson A, Dukes M, Kitaev S. Unlabeled (2+2)-free posets, ascent sequences and pattern avoiding permutations. 2009. Paper presented at 21st International Conference on Formal Power Series & Algebraic Combinatorics, Hagenberg, Austria.