Balázs Patkós

activity

20112026

most citedInduced and non-induced poset saturation problems

29 citations · 72 across the 26 of their papers we have counts for

collaborators

37 papers

math.CO2026

Chain Covers in the Boolean Lattice

Zoltán Lóránt Nagy, Balázs Patkós

For integers $1 \leq r \leq n + 1$ , let $N (n, r)$ denote the least number of chains in the Boolean lattice $B_{n} = 2^{[n]}$ that cover every strict $r$ -term chain. The case $r = 1$ is the clas…

math.CO2024

On a generalization of a result of Kleitman

Ryan R. Martin, Balázs Patkós

A classical result of Kleitman determines the maximum number $f (n, s)$ of subsets in a family $F \subseteq 2^{[n]}$ of sets that do not contain distinct sets $F_1,F_2,\dots…

math.CO2023

Projective and external saturation problem for posets

Dömötör Pálvölgyi, Balázs Patkós

We introduce two variants of the poset saturation problem. For a poset $P$ and the Boolean lattice $B_{n}$ , a family $F$ of sets, not necessarily from $\mathcal{B…

math.CO2020

Stability of extremal connected hypergraphs avoiding Berge-paths

Dániel Gerbner, Dániel T. Nagy, Balázs Patkós +2

A Berge-path of length $k$ in a hypergraph $H$ is a sequence $v_{1}, e_{1}, v_{2}, e_{2}, \dots, v_{k}, e_{k}, v_{k + 1}$ of distinct vertices and hyperedges with $v_{i}, v_{i + 1} \in e_{i}$ , f…

math.CO2020★ 29 cited

Induced and non-induced poset saturation problems

Balázs Keszegh, Nathan Lemons, Ryan R. Martin +2

A subfamily $G \subseteq F \subseteq 2^{[n]}$ of sets is a non-induced (weak) copy of a poset $P$ in $F$ if there exists a bijection $i:P\rightarrow \ma…

math.CO2019★ 3 cited

Some exact results for regular Turán problems

Dániel Gerbner, Balázs Patkós, Zsolt Tuza +1

As a variant of the famous Turán problem, we study $rex (n, F)$ , the maximum number of edges that an $n$ -vertex regular graph can have without containing a copy of $F$ . We d…