An obvious proof of Fishburn's interval order theorem
Discrete Mathematics
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
The Umbral transfer-matrix method. I: foundations
Journal of Combinatorial Theory Series A
A characterization of (3+1) - free posets
Journal of Combinatorial Theory Series A
Restricted permutations and the wreath product
Discrete Mathematics
Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
On a conjecture about enumerating (2+2)-free posets
European Journal of Combinatorics
Partition and composition matrices
Journal of Combinatorial Theory Series A
Enumerating (2+ 2)-free posets by the number of minimal elements and other statistics
Discrete Applied Mathematics
A polyominoes-permutations injection and tree-like convex polyominoes
Journal of Combinatorial Theory Series A
Counting general and self-dual interval orders
Journal of Combinatorial Theory Series A
Partitions and partial matchings avoiding neighbor patterns
European Journal of Combinatorics
Fishburn diagrams, Fishburn numbers and their refined generating functions
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Web worlds, web-colouring matrices, and web-mixing matrices
Journal of Combinatorial Theory Series A
Efficient generation of restricted growth words
Information Processing Letters
Ascent sequences and 3-nonnesting set partitions
European Journal of Combinatorics
On q-series identities related to interval orders
European Journal of Combinatorics
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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 31@?524@? and use this to enumerate those permutations, thereby settling a conjecture of Pudwell.