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- Mireille Bousquet-Mélou, Anders Claesson, Mark Dukes, Sergey Kitaev
- J. Comb. Theory, Ser. A
- 2010

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)

- Mark Dukes, Robert Parviainen
- Electr. J. Comb.
- 2010

This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijec-tion and prove that some of these statistics are equidistributed. Several special… (More)

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 chord diagrams (or involutions), already appear in the literature. The third one is a class of permutations, defined in terms of a new type of pattern. An attractive property of these patterns is that, like… (More)

- Fan Chung Graham, Anders Claesson, Mark Dukes, Ronald L. Graham
- Eur. J. Comb.
- 2010

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)

- Mark Dukes, Vít Jelínek, Martina Kubitzke
- Electr. J. Comb.
- 2011

In this paper we present a bijection between composition matrices and (2 + 2)-free posets. This bijection maps partition matrices to factorial posets, and induces a bijection from upper triangular matrices with non-negative entries having no rows or columns of zeros to unlabeled (2 + 2)-free posets. Chains in a (2 + 2)-free poset are shown to correspond to… (More)

- Mark Dukes, Yvan Le Borgne
- J. Comb. Theory, Ser. A
- 2013

In this paper we study a mapping from permutations to Dyck paths. A Dyck path gives rise to a (Young) diagram and we give relationships between statistics on permutations and statistics on their corresponding diagrams. The expectation and variance of the size of the diagram are also given. We propose a filling of the diagram which determines the permutation… (More)

In connection with Vassiliev's knot invariants, Stoimenow (1998) introduced certain matchings, also called regular linearized chord diagrams. Bousquet-Mélou et al. (2008) gave a bijection from those matchings to unlabeled (2 + 2)-free posets; they also showed how to encode the posets as so called ascent sequences. In this paper we present a direct encoding… (More)

- M N Graham Dukes
- Lancet
- 2002

The pharmaceutical industry is accountable on the one hand to its shareholders and on the other to the community at large. These two obligations can, in principle, be met. However, the industry has developed practices that do not consider society, including excessive or inappropriate pricing of drugs, an indifference to the needs and limitations of the… (More)

Let B be the operation of reordering a sequence by one pass of bubble sort. We completely answer the question of when the inverse image of a principal pattern class under B is a pattern class.