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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)

- Sergey Kitaev, Jeffrey B. Remmel
- Discrete Applied Mathematics
- 2011

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)

- Sergey Kitaev
- Discrete Mathematics
- 2005

- Sergey Kitaev, Toufik Mansour
- Ars Comb.
- 2005

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)

- Sergey V. Avgustinovich, Sergey Kitaev
- Discrete Mathematics
- 2008

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)

- Sergey Kitaev
- Monographs in Theoretical Computer Science. An…
- 2011

- Sergey Kitaev
- Discrete Mathematics
- 2003

It is well-known, and was first established by Knuth in 1969, that the number of 321-avoiding permutations is equal to that of 132-avoiding permutations. In the literature one can find many subsequent bijective proofs of this fact. It turns out that some of the published bijections can easily be obtained from others. In this paper we describe all bijections… (More)

Recently, Kitaev [9] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingrímsson [1]. A POGP p is a GP some of whose letters are incomparable. In this paper, we study the generating functions (g.f.) for the number of k-ary words… (More)

This paper is a continuation of the systematic study of the distribution of quadrant marked mesh patterns initiated by the authors in [J. We study quadrant marked mesh patterns on up-down and down-up permutations , also known as alternating and reverse alternating permutations, respectively. In particular, we refine classical enumeration results of André… (More)