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

Bousquet-Melou, Mireille and Claesson, Anders and Dukes, Mark and Kitaev, Sergey (2010) (2+2)-free posets, ascent sequences and pattern avoiding permutations. Journal of Combinatorial Theory Series A, 117 (7). pp. 884-909.

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Abstract

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not known to be equinumerous. We present a direct bijection between them. The third class is a family of permutations defined in terms of a new type of pattern. An attractive property of these patterns is that, like classical patterns, they are closed under the action of the symmetry group of the square. The fourth class is formed by certain integer sequences, called ascent sequences, which have a simple recursive structure and are shown to encode (2+2)-free posets and permutations. Our bijections preserve numerous statistics. We determine the generating function of these classes of objects, thus recovering a non-D-finite series obtained by Zagier for the class of chord diagrams. Finally, we characterize the ascent sequences that correspond to permutations avoiding the barred pattern View the MathML source and use this to enumerate those permutations, thereby settling a conjecture of Pudwell.

Item type: Article
ID code: 34502
Keywords: (2+2)-free poset, ascent sequences, pattern avoiding permutation, chord diagram, involution, encode, enumerate, non-D-finite series, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Computational Theory and Mathematics, Theoretical Computer Science
Subjects: Science > Mathematics > Electronic computers. Computer science
Department: Faculty of Science > Computer and Information Sciences
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 23 Oct 2011 05:14
    Last modified: 05 Sep 2014 12:02
    URI: http://strathprints.strath.ac.uk/id/eprint/34502

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