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pro vyhledávání: '"Makhul, Mehdi"'
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the corresponding edge l
Externí odkaz:
http://arxiv.org/abs/2403.00392
For every graph that is mimimally rigid in the plane, its Galois group is defined as the Galois group generated by the coordinates of its planar realizations, assuming that the edge lengths are transcendental and algebraically independent. Here we co
Externí odkaz:
http://arxiv.org/abs/2306.04392
Autor:
Makhul, Mehdi, Pinchasi, Rom
Let $P$ be a set of $n$ points in general position in the plane. Let $R$ be a set of points disjoint from $P$ such that for every $x,y \in P$ the line through $x$ and $y$ contains a point in $R$. We show that if $|R| < \frac{3}{2}n$ and $P \cup R$ is
Externí odkaz:
http://arxiv.org/abs/2110.06179
Autor:
Makhul, Mehdi, Winterhof, Arne
Let ${\mathbb F}_q$ be the finite field of $q$ elements, where $q=p^r$ is a power of the prime $p$, and $\left(\beta_1, \beta_2, \dots, \beta_r \right)$ be an ordered basis of ${\mathbb F}_q$ over ${\mathbb F}_p$. For $$\xi=\sum_{i=1}^rx_i\beta_i, \q
Externí odkaz:
http://arxiv.org/abs/2106.12218
In this paper we give a conditional improvement to the Elekes-Szab\'{o} problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}[x,y,z]$ belonging to a particular family of polynomials, and any
Externí odkaz:
http://arxiv.org/abs/2009.13258
Autor:
Makhul, Mehdi
A perfect triangle is a triangle with rational sides, medians, and area. In this article, we use a similar strategy due to Pocklington to show that if $\Delta$ is a perfect triangle, then it cannot be an isosceles triangle. It gives a partial answer
Externí odkaz:
http://arxiv.org/abs/2009.00654
We study subsets of the $n$-dimensional vector space over the finite field $\mathbb{F}_q$, for odd $q$, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets a
Externí odkaz:
http://arxiv.org/abs/2004.00904
Autor:
Makhul, Mehdi
Richard Guy asked the following question: can we find a triangle with rational sides, medians, and area? Such a triangle is called a \emph{perfect triangle} and no example has been found to date. It is widely believed that such a triangle does not ex
Externí odkaz:
http://arxiv.org/abs/1910.06888
We give a construction of a non-degenerate polynomial $F\in \mathbb R[x,y,z]$ and a set $A$ of cardinality $n$ such that $\left|Z(F)\cap (A \times A \times A) \right| \gg n^{\frac{3}{2}}$, thus providing a new lower bound construction for the Elekes-
Externí odkaz:
http://arxiv.org/abs/1812.00654
Autor:
Makhul, Mehdi, Schicho, Josef
Given an irreducible variety $X$ over a finite field, the density of hypersurfaces of varying degree $d$ intersecting $X$ in an irreducible subvariety is $1$, by a result of Charles and Poonen. In this note, we analyse the situation fixing $d=1$ and
Externí odkaz:
http://arxiv.org/abs/1809.04930