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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 bijection and prove that some of these statistics are equidistributed. Several special… (More)

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

- 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)

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)

- Rodger L. Bick, Mark Dukes, William L. Wilson, Lilla Fekete
- Thrombosis research
- 1977

- Tom S. Weber, Mark Dukes, Denise C. Miles, Stefan P. Glaser, Shalin H. Naik, Ken R. Duffy
- BMC Systems Biology
- 2016

Cellular barcoding is a recently developed biotechnology tool that enables the familial identification of progeny of individual cells in vivo. In immunology, it has been used to track the burst-sizes of multiple distinct responding T cells over several adaptive immune responses. In the study of hematopoiesis, it revealed fate heterogeneity amongst… (More)

Let B be the operation of re-ordering 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.

- Anders Claesson, Mark Dukes, Martina Kubitzke
- J. Comb. Theory, Ser. A
- 2011

Article history: Received 9 June 2010 Available online 16 February 2011