Zobrazeno 1 - 10
of 2 310
pro vyhledávání: '"SAGDEEV, A. A."'
Autor:
Dumitrescu, Adrian, Sagdeev, Arsenii
We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation sequences is e
Externí odkaz:
http://arxiv.org/abs/2411.13206
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 Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for every set o
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
Autor:
Sagdeev, Arsenii
We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by T\'oth in 1997.
Comment: 13 pages, 21 figures; a few modifications based
Comment: 13 pages, 21 figures; a few modifications based
Externí odkaz:
http://arxiv.org/abs/2402.09131
Publikováno v:
Discrete & Computational Geometry (2024)
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