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- Sergey Kitaev
- Discrete Mathematics
- 2005

- 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) ) . We extend this result by… (More)

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

In this paper we begin the first systematic study of distributions of quadrant marked mesh patterns. Mesh patterns were introduced recently by Brändén and Claesson in connection with permutation statistics. Quadrant marked mesh patterns are based on how many elements lie in various quadrants of the graph of a permutation relative to the coordinate system… (More)

- Sergey Kitaev
- Discrete Mathematics
- 2003

Recently, Kitaev [9] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingrı́msson [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)

- Sergey Kitaev, Artem V. Pyatkin
- Journal of Automata, Languages and Combinatorics
- 2008

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x 6= y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. Examples of non-representable graphs are found in this paper. Some wide classes of graphs are… (More)

- Sergey Kitaev
- Discrete Applied Mathematics
- 2007

We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multiand shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide several (new) results on a class of POPs built on an arbitrary flat poset, obtaining, as corollaries, the bivariate… (More)

In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We… (More)