Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Zakharov, Dmitrii"'
Autor:
Pham, Huy Tuan, Zakharov, Dmitrii
A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$. We show that the largest non-averaging subset of $\{1, \ldots, n\}$ has size $n^{1/4+o(1)}$, thus solvi
Externí odkaz:
http://arxiv.org/abs/2410.14624
Let $p_1,\ldots,p_n$ be a set of points in the unit square and let $T_1,\ldots,T_n$ be a set of $\delta$-tubes such that $T_j$ passes through $p_j$. We prove a lower bound for the number of incidences between the points and tubes under a natural regu
Externí odkaz:
http://arxiv.org/abs/2409.07658
Autor:
Pach, János, Zakharov, Dmitrii
A subset $S$ of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of $S$ are distinct. Imre Ruzsa asked the following question: What
Externí odkaz:
http://arxiv.org/abs/2409.03128
Autor:
Łaba, Izabella, Zakharov, Dmitrii
If a finite set $A$ tiles the integers by translations, it also admits a tiling whose period $M$ has the same prime factors as $|A|$. We prove that the minimal period of such a tiling is bounded by $\exp(c(\log D)^2/\log\log D)$, where $D$ is the dia
Externí odkaz:
http://arxiv.org/abs/2406.14824
Autor:
Zakharov, Dmitrii
We show that if $A$ is a set of mutually orthogonal exponentials with respect to the unit disk then $|A \cap [-R, R]^2| \lesssim_\varepsilon R^{3/5+\varepsilon}$ holds. This improves the previous bound of $R^{2/3}$ by Iosevich--Kolountzakis. The main
Externí odkaz:
http://arxiv.org/abs/2405.14063
We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots\}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon > 0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] T
Externí odkaz:
http://arxiv.org/abs/2405.08650
Autor:
Zakharov, Dmitrii
For $g \ge 2$, we show that the number of positive integers at most $X$ which can be written as sum of two base $g$ palindromes is at most $\frac{X}{\log^c X}$. This answers a question of Baxter, Cilleruelo and Luca.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2402.10808
Autor:
Pohoata, Cosmin, Zakharov, Dmitrii
We construct skew corner-free sets in $[n]^2$ of size $n^{5/4}$, thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in $\mathbb{F}_{q}^{n} \times \mathbb{F}_{q}^{n}$ must have size at most $q^{(2-c)n}$, for som
Externí odkaz:
http://arxiv.org/abs/2401.17507
Autor:
Zakharov, Dmitrii
We show that there exists an absolute constant $c_0<1$ such that for all $n \ge 2$, any set $A \subset S^{n-1}$ of density at least $c_0$ contains $n$ pairwise orthogonal vectors. The result is sharp up to the value of the constant $c_0$. The proof r
Externí odkaz:
http://arxiv.org/abs/2310.06821
Autor:
Sauermann, Lisa, Zakharov, Dmitrii
We prove essentially sharp bounds for Ramsey numbers of ordered hypergraph matchings, inroduced recently by Dudek, Grytczuk, and Ruci\'{n}ski. Namely, for any $r \ge 2$ and $n \ge 2$, we show that any collection $\mathcal H$ of $n$ pairwise disjoint
Externí odkaz:
http://arxiv.org/abs/2309.04813