Zobrazeno 1 - 10
of 33
pro vyhledávání: '"White, Ethan Patrick"'
Autor:
Balogh, Jozsef, White, Ethan Patrick
Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2 n\log n)$. In particular, ever
Externí odkaz:
http://arxiv.org/abs/2404.02369
We present a general method to modify existing uniquely decodable codes in the $T$-user binary adder channel. If at least one of the original constituent codes does not have average weight exactly half of the dimension, then our method produces a new
Externí odkaz:
http://arxiv.org/abs/2312.11723
For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to the original body. A classical result states that the Kovner-Besicovitch
Externí odkaz:
http://arxiv.org/abs/2309.12597
Autor:
Martin, Greg, Yang, Pu Justin Scarfy, Bahrini, Aram, Bajpai, Prajeet, Benli, Kübra, Downey, Jenna, Li, Yuan Yuan, Liang, Xiaoxuan, Parvardi, Amir, Simpson, Reginald, White, Ethan Patrick, Yip, Chi Hoi
The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We use a unified system of notation for the quantities being studied and
Externí odkaz:
http://arxiv.org/abs/2309.08729
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
Comment: 8 pages, 1 figure
Comment: 8 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2304.03920
Let $\mathcal{P}$ be a set of points in the plane, and $\mathcal{S}$ a strictly convex set of points. In this note, we show that if $\mathcal{P}$ contains many translates of $\mathcal{S}$, then these translates must come from a generalized arithmetic
Externí odkaz:
http://arxiv.org/abs/2302.13949
Autor:
White, Ethan Patrick
Let $\mathcal{F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb{R}$ such that $\int f = 1$. We determine the value of $\inf_{f \in \mathcal{F}} \| f \ast f \|_2$ up to a 0.0014\% error, thereby making progress on a problem asked by Ben
Externí odkaz:
http://arxiv.org/abs/2210.16437
Autor:
White, Ethan Patrick
We obtain a substantially improved lower bound for the minimum overlap problem asked by Erd\H{o}s. Our approach uses elementary Fourier analysis to translate the problem to a convex optimization program.
Comment: 27 pages, 2 figures, 8 tables
Comment: 27 pages, 2 figures, 8 tables
Externí odkaz:
http://arxiv.org/abs/2201.05704
Publikováno v:
Mathematika 68 (2022), no. 2, 511-534
Let $p$ be a prime and $n$ a positive integer such that $\sqrt{\frac p2} + 1 \leq n \leq \sqrt{p}$. For any arithmetic progression $A$ of length $n$ in $\mathbb{F}_p$, we establish an asymptotic formula for the number of directions determined by $A \
Externí odkaz:
http://arxiv.org/abs/2107.01311
Publikováno v:
In European Journal of Combinatorics May 2024 118
