Zobrazeno 1 - 10
of 2 079
pro vyhledávání: '"A A Sagdeev"'
For a positive integer $g$, we study a family of plane graphs $G$ without cycles of length less than $g$ that are maximal in a sense that adding any new edge to $G$ either makes it non-plane or creates a cycle of length less than $g$. We show that th
Externí odkaz:
http://arxiv.org/abs/2410.13481
For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding op
Externí odkaz:
http://arxiv.org/abs/2407.01101
For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Yao graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for every set of $n$ points
Externí odkaz:
http://arxiv.org/abs/2406.08913
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are looking for an
Externí odkaz:
http://arxiv.org/abs/2404.11454
We prove that for any $\ell_p$-norm in the plane with $1
Externí odkaz:
http://arxiv.org/abs/2308.08840
Publikováno v:
Doklady Mathematics, 2024, Vol. 109, No. 1, pp. 80--83
In 1993, Kahn and Kalai famously constructed a sequence of finite sets in $d$-dimensional Euclidean spaces that cannot be partitioned into less than $(1.203\ldots+o(1))^{\sqrt{d}}$ parts of smaller diameter. Their method works not only for the Euclid
Externí odkaz:
http://arxiv.org/abs/2307.09854
Publikováno v:
European Journal of Combinatorics, 2024, Vol. 120, 103977, 11 pp
For all non-degenerate triangles T, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of T is monochromatic.
Comment: 10 pages, 4 figures; v2 includes a few modifications based on the review
Comment: 10 pages, 4 figures; v2 includes a few modifications based on the review
Externí odkaz:
http://arxiv.org/abs/2302.09972
We say that a subset $M$ of $\mathbb R^n$ is exponentially Ramsey if there are $\epsilon>0$ and $n_0$ such that $\chi(\mathbb R^n,M)\ge(1+\epsilon)^n$ for any $n>n_0$, where $\chi(\mathbb R^n,M)$ stands for the minimum number of colors in a coloring
Externí odkaz:
http://arxiv.org/abs/2211.17150
Publikováno v:
Revista Matem\'atica Iberoamericana, 2024, Vol. 40, No. 2, pp. 637--648
We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(\sqrt{2} + o(1))\sqrt{p}$ distinct residues modulo prime $p$. Moreover, factorials on an interval $\mathcal{I} \subseteq \{0, 1, \dots, p - 1\}$ of length $N > p^{7/8 + \varepsilon}$
Externí odkaz:
http://arxiv.org/abs/2204.01153
Autor:
Kirova, Valeriya, Sagdeev, Arsenii
Publikováno v:
SIAM Journal on Discrete Mathematics, 2023, Vol. 37, No. 2, pp. 718--732
Given a natural $n$, we construct a two-coloring of $\mathbb{R}^n$ with the maximum metric satisfying the following. For any finite set of reals $S$ with diameter greater than $5^{n}$ such that the distance between any two consecutive points of $S$ d
Externí odkaz:
http://arxiv.org/abs/2203.04555