Zobrazeno 1 - 10
of 124
pro vyhledávání: '"LUND, BEN"'
We give an upper bound on the number of exceptional orthogonal projections of a small set of points in a plane over a prime order field, which makes progress toward a conjecture of Chen (2018). This theorem relies on a new upper bound on the number o
Externí odkaz:
http://arxiv.org/abs/2311.05148
A conjecture on radial projections in $\mathbb{F}_q^d$ states that if $E\subset \mathbb{F}_q^n$ with $q^{k-1}< |E|\leq q^{k}$ for some $k \in \{1,\dots, n-1\}$, then \[ \#\{y\in \mathbb{F}_q^n \mid |\pi^y(E)| < |E| \} \leq q^k. \] The case $k=n-1$ wa
Externí odkaz:
http://arxiv.org/abs/2311.05127
We give a construction of a convex set $A \subset \mathbb R$ with cardinality $n$ such that $A-A$ contains a convex subset with cardinality $\Omega (n^2)$. We also consider the following variant of this problem: given a convex set $A$, what is the si
Externí odkaz:
http://arxiv.org/abs/2309.07527
Autor:
Chakraborti, Debsoumya, Lund, Ben
For $d\ge 2$ and an odd prime power $q$, consider the vector space $\mathbb{F}_q^d$ over the finite field $\mathbb{F}_q$, where the distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined as $\sum_{i=1}^d (x_i-y_i)^2$. A dist
Externí odkaz:
http://arxiv.org/abs/2306.12023
We call an edge-colored graph rainbow if all of its edges receive distinct colors. An edge-colored graph $\Gamma$ is called $H$-rainbow saturated if $\Gamma$ does not contain a rainbow copy of $H$ and adding an edge of any color to $\Gamma$ creates a
Externí odkaz:
http://arxiv.org/abs/2212.04640
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen (2016), Orponen
Externí odkaz:
http://arxiv.org/abs/2205.07431
The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an
Externí odkaz:
http://arxiv.org/abs/2203.12801
Autor:
Balogh, József, Chen, Ce, Hendrey, Kevin, Lund, Ben, Luo, Haoran, Tompkins, Casey, Tran, Tuan
A family $\mathcal{F}$ on ground set $[n]:=\{1,2,\ldots, n\}$ is maximal $k$-wise intersecting if every collection of at most $k$ sets in $\mathcal{F}$ has non-empty intersection, and no other set can be added to $\mathcal{F}$ while maintaining this
Externí odkaz:
http://arxiv.org/abs/2110.12708
Autor:
Lund, Ben, Reichman, Daniel
We give a simple proof that every $n$-vertex graph $d$-regular graph that does not contain a fixed bipartite graph as a subgraph has an induced matching of size $\Omega((n/d)(\log d))$.
Externí odkaz:
http://arxiv.org/abs/2006.03225
Autor:
Lund, Ben, Potukuchi, Aditya
We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that
Externí odkaz:
http://arxiv.org/abs/2005.02478