Zobrazeno 1 - 10
of 367
pro vyhledávání: '"KITAEV, SERGEY"'
In this paper, we propose a general framework that extends the theory of permutation patterns to higher dimensions and unifies several combinatorial objects studied in the literature. Our approach involves introducing the concept of a "level" for an
Externí odkaz:
http://arxiv.org/abs/2411.02897
In this paper, we find distributions of the left-to-right maxima, right-to-left maxima, left-to-right minima and right-to-left-minima statistics on up-down and down-up permutations of even and odd lengths. For instance, we show that the distribution
Externí odkaz:
http://arxiv.org/abs/2408.12865
Autor:
Kitaev, Sergey, Lv, Shuzhen
A notable problem within permutation patterns that has attracted considerable attention in literature since 1973 is the search for a bijective proof demonstrating that 123-avoiding and 132-avoiding permutations are equinumerous, both counted by the C
Externí odkaz:
http://arxiv.org/abs/2408.09401
Autor:
Kitaev, Sergey, Qiu, Dun
A universal cycle (u-cycle) for permutations of length $n$ is a cyclic word, any size $n$ window of which is order-isomorphic to exactly one permutation of length $n$, and all permutations of length $n$ are covered. It is known that u-cycles for perm
Externí odkaz:
http://arxiv.org/abs/2408.05984
Autor:
Kitaev, Sergey, Pyatkin, Artem
An orientation of a graph is semi-transitive if it contains no directed cycles and has no shortcuts. An undirected graph is semi-transitive if it can be oriented in a semi-transitive manner. The class of semi-transitive graphs includes several import
Externí odkaz:
http://arxiv.org/abs/2408.05066
The notion of a $k$-11-representable graph was introduced by Jeff Remmel in 2017 and studied by Cheon et al.\ in 2019 as a natural extension of the extensively studied notion of word-representable graphs, which are precisely 0-11-representable graphs
Externí odkaz:
http://arxiv.org/abs/2407.17784
We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns {12345,12354} and {45123,45213} that extends the list of 10 related conjectures proved in the literature in a series of papers. To achieve our goals, we prove generalized
Externí odkaz:
http://arxiv.org/abs/2405.14041
We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable permutations. The equa
Externí odkaz:
http://arxiv.org/abs/2404.18517
Autor:
Bonato, Andrea, Corbett, Dom, Kitaev, Sergey, Marenduzzo, Davide, Morozov, Alexander, Orlandini, Enzo
The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fibre is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA po
Externí odkaz:
http://arxiv.org/abs/2312.12159
Autor:
Bonato, Andrea, Corbett, Dom, Kitaev, Sergey, Marenduzzo, Davide, Morozov, Alexander, Orlandini, Enzo
Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, bo
Externí odkaz:
http://arxiv.org/abs/2312.12154