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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)
We call a Stieltjes continued fraction with monic monomial numerators a Catalan continued fraction. Let e k (π) be the number of increasing subsequences of length k + 1 in the permutation π. We prove that any Cata-lan continued fraction is the multivariate generating function of a family of statistics on the 132-avoiding permutations, each consisting of a(More)
Motivated by juggling sequences and bubble sort, we examine permutations on the set {1, 2,. .. , n} with d descents and maximum drop size k. We give explicit formulas for enumerating such permutations for given integers k and d. We also derive the related generating functions and prove unimodality and symmetry of the coefficients. Résumé. Motivés par les "(More)
Any permutation statistic f : S → C may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: f = Σ τ λ f (τ)τ. To provide explicit expansions for certain statistics, we introduce a new type of permutation patterns that we call mesh patterns. Intuitively, an occurrence of the mesh pattern p = (π, R) is an(More)
Babson and Steingrímsson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Subsequently, Claesson presented a complete solution for the number of permutations avoiding any single pattern of type (1, 2) or (2, 1). For eight of these twelve patterns the answer is(More)
Although there is a need for antibacterial agents that act only on Gram-negative bacteria, there are at present few such compounds. The 2-deoxy analogue of beta-KDO (3-deoxy-beta-D-manno-2-octulopyranosonic acid) is a potent inhibitor of a key enzyme (CMP-KDO synthetase) in lipopolysaccharide biosynthesis of Gram-negative bacteria, but it fails to penetrate(More)