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pro vyhledávání: '"Pór, Attila"'
One of the most important and useful examples in discrete geometry is a finite sequence of points on the moment curve $\gamma(t)=(t,t^2,t^3,\dots ,t^d)$ or, more generally, on a {\it strictly monotone curve} in $\mathbb R^d$. These sequences as well
Externí odkaz:
http://arxiv.org/abs/2110.12474
We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$
Externí odkaz:
http://arxiv.org/abs/2103.13185
Autor:
Biró, Csaba, Hamburger, Peter, Kierstead, H. A., Pór, Attila, Trotter, William T., Wang, Ruidong
Previously, Erd\H{o}s, Kierstead and Trotter investigated the dimension of random height~$2$ partially ordered sets. Their research was motivated primarily by two goals: (1)~analyzing the relative tightness of the F\"{u}redi-Kahn upper bounds on dime
Externí odkaz:
http://arxiv.org/abs/2003.07935
Autor:
Por, Attila
A result of Rosenthal says that for every $q>1$ and $n \in \mathbb{N}$ there is $N \in \mathbb{N}$ such that every sequence of $N$ distinct positive numbers contains, after a suitable translation and possible multiplication by $-1$, a subsequence $a_
Externí odkaz:
http://arxiv.org/abs/1805.07197
For a positive integer $d$, a set of points in $d$-dimensional Euclidean space is called almost-equidistant if for any three points from the set, some two are at unit distance. Let $f(d)$ denote the largest size of an almost-equidistant set in $d$-sp
Externí odkaz:
http://arxiv.org/abs/1706.06375
A semiorder is a model of preference relations where each element $x$ is associated with a utility value $\alpha(x)$, and there is a threshold $t$ such that $y$ is preferred to $x$ iff $\alpha(y) > \alpha(x)+t$. These are motivated by the notion that
Externí odkaz:
http://arxiv.org/abs/1702.06614
Autor:
Edelman, Paul H., Por, Attila
Publikováno v:
In Games and Economic Behavior November 2021 130:443-451
Autor:
Magazinov, Alexander, Pór, Attila
Let $\mu$ be a Borel probability measure in $\mathbb R^d$. For a $k$-flat $\alpha$ consider the value $\inf \mu(H)$, where $H$ runs through all half-spaces containing $\alpha$. This infimum is called the half-space depth of $\alpha$. Bukh, Matou\v{s}
Externí odkaz:
http://arxiv.org/abs/1603.01641
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The dimension of a poset $P$, denoted $\dim(P)$, is the least positive integer $d$ for which $P$ is the intersection of $d$ linear extensions of $P$. The maximum dimension of a poset $P$ with $|P|\le 2n+1$ is $n$, provided $n\ge2$, and this inequalit
Externí odkaz:
http://arxiv.org/abs/1402.5113