Benedek Kovács

collaborators

5 papers

math.CO2025

Cardinalities of the total number of independent sets

Benedek KovÃ¡cs, ZoltÃ¡n LÃ³rÃ¡nt Nagy

We study the set of numbers the total number of independent sets can admit in $n$ -vertex graphs. In this paper, we prove that the cardinality $N i (n)$ of this set is very…

math.CO2025

Randomised algebraic constructions for the no- $(k + 1)$ -in-line problem

Benedek KovÃ¡cs, ZoltÃ¡n LÃ³rÃ¡nt Nagy, DÃ¡vid R. SzabÃ³

The no-(k+1)-in line problem seeks the maximum number of points that can be selected from an $n \times n$ square lattice such that no $k + 1$ of them are collinear. The problem was f…

math.CO2025

Code-based $[3, 1]$ -avoiders in finite affine spaces $AG (n, 2)$

Benedek KovÃ¡cs

The author, together with Nagy, studied the following problem on unavoidable intersections of given size in binary affine spaces. Given an $m$ -element set $S\subseteq \mathbb{F}_2^…

math.CO2025

The generalized trifference problem

Anurag Bishnoi, BartÅomiej Kielak, Benedek KovÃ¡cs +4

We study the problem of finding the largest number $T (n, m)$ of ternary vectors of length $n$ such that for any three distinct vectors there are at least $m$ coordinates where they…

math.CO2025

Settling the no- $(k + 1)$ -in-line problem when $k$ is not small

Benedek KovÃ¡cs, ZoltÃ¡n LÃ³rÃ¡nt Nagy, DÃ¡vid R. SzabÃ³

What is the maximum number of points that can be selected from an $n \times n$ square lattice such that no $k + 1$ of them are in a line? This has been asked more than $100$ years ag…

Cardinalities of the total number of independent sets

Randomised algebraic constructions for the no-(k+1)-in-line problem

Code-based [3,1]-avoiders in finite affine spaces AG(n,2)

The generalized trifference problem

Settling the no-(k+1)-in-line problem when k is not small

Randomised algebraic constructions for the no- $(k + 1)$ -in-line problem

Code-based $[3, 1]$ -avoiders in finite affine spaces $AG (n, 2)$

Settling the no- $(k + 1)$ -in-line problem when $k$ is not small