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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… (More)

A poset is said to be (2 + 2)-free if it does not contain an induced subposet that is isomorphic to 2 + 2, the union of two disjoint 2-element chains. In a recent paper, Bousquet-Mélou et al. found, using so called ascent sequences, the generating function for the number of (2 + 2)-free posets: P (t) = n≥0 n i=1 1 − (1 − t) i. We extend this result by… (More)

In [BabStein] Babson and Steingrímsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In [Kit1] Kitaev considered simultaneous avoidance (multi-avoidance) of two or more 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous… (More)

In [5] the authors refine the well-known permutation statistic " descent " by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the first or the second element in a descent pair is equivalent to k mod k ≥ 2. We provide either an explicit or an… (More)

Motivated by a new point of view to study occurrences of consecutive patterns in permutations, we introduce the notion of uniquely k-determined permutations. We give two criteria for a permutation to be uniquely k-determined: one in terms of the distance between two consecutive elements in a permutation, and the other one in terms of directed hamiltonian… (More)

Dedication. This paper is dedicated to Anders Björner on the occasion of his 60th birthday. His work has very heavily influenced ours. Abstract Let P be a partially ordered set and consider the free monoid P * of all words over P. If w, w ′ ∈ P * then w ′ is a factor of w if there are words u, v with w = uw ′ v. Define generalized factor order on P * by… (More)

The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for… (More)