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pro vyhledávání: '"Kovács, Benedek"'
In this paper, we study the cardinality of the smallest set of lines of the finite projective spaces $\operatorname{PG}(n,q)$ such that every plane is incident with at least one line of the set. This is the first main open problem concerning the mini
Externí odkaz:
http://arxiv.org/abs/2410.07937
Autor:
Kovács, Benedek
We consider the following question by Balister, Gy\H{o}ri and Schelp: given $2^{n-1}$ nonzero vectors in $\mathbb{F}_2^n$ with zero sum, is it always possible to partition the elements of $\mathbb{F}_2^n$ into pairs such that the difference between t
Externí odkaz:
http://arxiv.org/abs/2310.17433
Autor:
Britto, Ricardo, Murphy, Timothy, Iovene, Massimo, Jonsson, Leif, Erol-Kantarci, Melike, Kovács, Benedek
The rapid advancements in Artificial Intelligence (AI), particularly in generative AI and foundational models (FMs), have ushered in transformative changes across various industries. Large language models (LLMs), a type of FM, have demonstrated their
Externí odkaz:
http://arxiv.org/abs/2310.11770
Autor:
Elsholtz, Christian, Führer, Jakob, Füredi, Erik, Kovács, Benedek, Pach, Péter Pál, Simon, Dániel Gábor, Velich, Nóra
We study subsets of $\mathbb{F}_p^n$ that do not contain progressions of length $k$. We denote by $r_k(\mathbb{F}_p^n)$ the cardinality of such subsets containing a maximal number of elements. In this paper we focus on the case $k=p$ and therefore se
Externí odkaz:
http://arxiv.org/abs/2310.03382
Autor:
Kovács, Benedek, Nagy, Zoltán Lóránt
We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m \in [0, 2^n] of the n-dimensional binary affine space AG(n,2). Following the theme of Erd\H{o}s, F\"uredi, Rothschild and T. S\'os, we partially deter
Externí odkaz:
http://arxiv.org/abs/2305.05632
In this paper, we study a Ramsey-type problem for equations of the form $ax+by=p(z)$. We show that if certain technical assumptions hold, then any 2-colouring of the positive integers admits infinitely many monochromatic solutions to the equation $ax
Externí odkaz:
http://arxiv.org/abs/2209.09334
Autor:
Kovács, Benedek, Nagy, Zoltán Lóránt
In this paper we continue the study of a natural generalization of Tur\'an's forbidden subgraph problem and the Ruzsa-Szemer\'edi problem. Let $ex_F(n,G)$ denote the maximum number of edge-disjoint copies of a fixed simple graph $F$ that can be place
Externí odkaz:
http://arxiv.org/abs/2207.14572
Autor:
Kovács, Benedek, Nagy, Zoltán Lóránt
Publikováno v:
In Journal of Combinatorial Theory, Series A January 2025 209
Akademický článek
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Publikováno v:
In Discrete Mathematics May 2023 346(5)