Zobrazeno 1 - 10
of 5 016
pro vyhledávání: '"Pach, A"'
Autor:
Nagy, János, Pach, Péter Pál
Pilz's conjecture states that for any finite set $A=\{a_1,a_2,\dots,a_k\}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values
Externí odkaz:
http://arxiv.org/abs/2409.15075
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
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.
Comment: This is a survey paper
Comment: This is a survey paper
Externí odkaz:
http://arxiv.org/abs/2408.02328
A curve in the plane is $x$-monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point in common. We construct $2^{\Omega(n^{4/3})}$ families, each consisting
Externí odkaz:
http://arxiv.org/abs/2405.20547
Autor:
Dumitrescu, Adrian, Pach, János
A \emph{complete geometric graph} consists of a set $P$ of $n$ points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a positive c
Externí odkaz:
http://arxiv.org/abs/2405.17172
Prototypical parts networks combine the power of deep learning with the explainability of case-based reasoning to make accurate, interpretable decisions. They follow the this looks like that reasoning, representing each prototypical part with patches
Externí odkaz:
http://arxiv.org/abs/2405.14331
Let $F_{k,d}(n)$ be the maximal size of a set ${A}\subseteq [n]$ such that the equation \[a_1a_2\dots a_k=x^d, \; a_1
Externí odkaz:
http://arxiv.org/abs/2405.12088
Liu, Pach and S\'andor recently characterized all polynomials $p(z)$ such that the equation $x+y=p(z)$ is $2$-Ramsey, that is, any $2$-coloring of $\mathbb{N}$ contains infinitely many monochromatic solutions for $x+y=p(z)$. In this paper, we find as
Externí odkaz:
http://arxiv.org/abs/2404.00794
We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n \geq 12$ po
Externí odkaz:
http://arxiv.org/abs/2312.09916
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such that almo
Externí odkaz:
http://arxiv.org/abs/2312.01028