Zobrazeno 1 - 10
of 222
pro vyhledávání: '"Suk, Andrew"'
A curve in the plane is $x$-monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point in common. We construct $2^{\Omega(n^{4/3})}$ families, each consisting
Externí odkaz:
http://arxiv.org/abs/2405.20547
Let $ES_{\ell}(n)$ be the minimum $N$ such that every $N$-element point set in the plane contains either $\ell$ collinear members or $n$ points in convex position. We prove that there is a constant $C>0$ such that, for each $\ell, n \ge 3$, $$ (3\ell
Externí odkaz:
http://arxiv.org/abs/2405.03455
Autor:
Conlon, David, Fox, Jacob, He, Xiaoyu, Mubayi, Dhruv, Pham, Huy Tuan, Suk, Andrew, Verstraëte, Jacques
Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit const
Externí odkaz:
http://arxiv.org/abs/2404.16016
Autor:
Conlon, David, Fox, Jacob, Gunby, Benjamin, He, Xiaoyu, Mubayi, Dhruv, Suk, Andrew, Verstraete, Jacques
A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r(H, K_n^{(3)})$ of a fixed $3$-uniform hypergraph $H$ versus the complete $3$-uniform hypergraph with $n$ vertices. We study this problem, p
Externí odkaz:
http://arxiv.org/abs/2404.02021
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such that almo
Externí odkaz:
http://arxiv.org/abs/2312.01028
Autor:
Suk, Andrew, Zeng, Ji
As a variant of the celebrated Szemer\'edi--Trotter theorem, Guth and Katz proved that $m$ points and $n$ lines in $\mathbb{R}^3$ with at most $\sqrt{n}$ lines in a common plane must determine at most $O(m^{1/2}n^{3/4})$ incidences for $n^{1/2}\leq m
Externí odkaz:
http://arxiv.org/abs/2311.04804
Autor:
Suk, Andrew
Let $h(n)$ be the minimum integer such that every complete $n$-vertex simple topological graph contains an edge that crosses at most $h(n)$ other edges. In 2009, Kyn\v{c}l and Valtr showed that $h(n) = O(n^2/\log^{1/4} n)$, and in the other direction
Externí odkaz:
http://arxiv.org/abs/2307.08165
Autor:
Mubayi, Dhruv, Suk, Andrew
One formulation of the Erdos-Szekeres monotone subsequence theorem states that for any red/blue coloring of the edge set of the complete graph on $\{1, 2, \ldots, N\}$, there exists a monochromatic red $s$-clique or a monochromatic blue increasing pa
Externí odkaz:
http://arxiv.org/abs/2303.16995
Autor:
Hubard, Alfredo, Suk, Andrew
Given a complete simple topological graph $G$, a $k$-face generated by $G$ is the open bounded region enclosed by the edges of a non-self-intersecting $k$-cycle in $G$. Interestingly, there are complete simple topological graphs with the property tha
Externí odkaz:
http://arxiv.org/abs/2212.01311
Autor:
Suk, Andrew, Zeng, Ji
A finite point set in $\mathbb{R}^d$ is in general position if no $d + 1$ points lie on a common hyperplane. Let $\alpha_d(N)$ be the largest integer such that any set of $N$ points in $\mathbb{R}^d$ with no $d + 2$ members on a common hyperplane, co
Externí odkaz:
http://arxiv.org/abs/2211.15968