Zobrazeno 1 - 10
of 107
pro vyhledávání: '"Ambrus, Gergely"'
Autor:
Ambrus, Gergely, Gárgyán, Barnabás
We study the $(n-1)$-dimensional volume of central hyperplane sections of the $n$-dimensional cube $Q_n$. Our main goal is two-fold: first, we provide an alternative, simpler argument for proving that the volume of the section perpendicular to the ma
Externí odkaz:
http://arxiv.org/abs/2307.03792
Autor:
Ambrus, Gergely, Bozzai, Rainie
We extend classical estimates for the vector balancing constant of $\mathbb{R}^d$ equipped with the Euclidean and the maximum norms proved in the 1980's by showing that for $p =2$ and $p=\infty$, given vector families $V_1, \ldots, V_n \subset B_p^d$
Externí odkaz:
http://arxiv.org/abs/2302.10865
Given a set $S \subseteq \mathbb{R}^2$, define the \emph{Helly number of $S$}, denoted by $H(S)$, as the smallest positive integer $N$, if it exists, for which the following statement is true: for any finite family $\mathcal{F}$ of convex sets in~$\m
Externí odkaz:
http://arxiv.org/abs/2301.04683
Autor:
Ambrus, Gergely1,2 (AUTHOR) ambrus@renyi.hu, Csiszárik, Adrián2,3 (AUTHOR), Matolcsi, Máté2,4 (AUTHOR), Varga, Dániel2 (AUTHOR), Zsámboki, Pál2 (AUTHOR)
Publikováno v:
Mathematical Programming. Sep2024, Vol. 207 Issue 1/2, p303-327. 25p.
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erd\H{o}s that the density of any measurable planar set avoiding unit distances cannot exceed $1/4$. Our argument implies the upper bound of $0.2470$.
Externí odkaz:
http://arxiv.org/abs/2207.14179
Autor:
Ambrus, Gergely
We present a streamlined proof of K. Ball's symmetric plank theorem in $\mathbb{R}^d$, which solves the affine plank problem raised by Th. Bang for symmetric convex bodies.
Comment: Lemma 2 is incorrect
Comment: Lemma 2 is incorrect
Externí odkaz:
http://arxiv.org/abs/2203.11260
Autor:
Ambrus, Gergely
We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions. In particul
Externí odkaz:
http://arxiv.org/abs/2201.08823
Publikováno v:
SIAM Journal on Discrete Mathematics, 37, no. 3, 1457-1471. (2023)
We consider the minimum number of lines $h_n$ and $p_n$ needed to intersect or pierce, respectively, all the cells of the $n \times n$ chessboard. Determining these values can also be interpreted as a strengthening of the classical plank problem for
Externí odkaz:
http://arxiv.org/abs/2111.09702
Publikováno v:
Discrete and Computational Geometry, 2022+
We prove the following sparse approximation result for polytopes. Assume that $Q$ is a polytope in John's position. Then there exist at most $2d$ vertices of $Q$ whose convex hull $Q'$ satisfies $Q \subseteq - 2d^2 \, Q'$. As a consequence, we retrie
Externí odkaz:
http://arxiv.org/abs/2108.05745