Balázs Patkós

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20112026

most citedSet systems related to a house allocation problem

6 citations · 16 across the 19 of their papers we have counts for

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Showing 2026 · math.COShow all

6 papers · 2 filters

math.CO2026

Forbidden subposet problems in the linear lattice

Balázs Patkós, Casey Tompkins

We study weak and strong forbidden subposet problems in the linear lattice $L_{n} (q)$ . We show that the $q$ -analogues of the Bukh--Griggs--Lu conjecture fail for every prime power $q…

math.CO2026

Embedding rooted blow-ups of tree posets

Balázs Patkós

A tree poset $T$ is a poset whose Hasse diagram is a tree. Bukh proved that if a family $F \subseteq 2^{[n]}$ contains $(h(T)-1+\varepsilon)\binom{n}{\lfloor \frac{n}{2}\rf…

math.CO2026

Maximal anti-Ramsey problems for posets

Binlong Li, Balázs Patkós, Changxin Wang

We study the forbidden poset analog of the maximal anti-Ramsey problem introduced for graphs by Burr, Erd\H os, Graham, and Sós. For integers $m \leq 2^{n}$ and poset $P = (P, ⪯)$ ,…

math.CO2026

Crown-free families and forbidden subposets with $e (P) \in {1, 2}$

Balázs Patkós, Casey Tompkins

The maximum size of a weak $P$ -free family $F \subseteq 2^{[n]}$ is denoted by $L a (n, P)$ . Let $e (P)$ denote the maximum integer $k$ such that the union of any $k$ consecut…

math.CO2026

On the maximum size of $B_{3}$ -free and $D_{s}$ -free families

Balázs Patkós

For a poset $P$ , let $e (P)$ ( $e^{*} (P)$ ) denote largest positive integer $k$ such that the union of the $k$ middle layers of $2^{[n]}$ does not contain a weak (strong) copy of $P$ . E…

math.CO2026

Anti-Ramsey forbidden poset problems

Balázs Patkós

A family $G$ of sets is a weak copy of a poset $P$ if there is a bijection $f : P \to G$ such that $p ⩽ q$ implies $f (p) \subseteq f (q)$ . If $f$ sati…

Forbidden subposet problems in the linear lattice

Embedding rooted blow-ups of tree posets

Maximal anti-Ramsey problems for posets

Crown-free families and forbidden subposets with e(P)∈{1,2}

On the maximum size of B3​-free and Ds​-free families

Anti-Ramsey forbidden poset problems

Crown-free families and forbidden subposets with $e (P) \in {1, 2}$

On the maximum size of $B_{3}$ -free and $D_{s}$ -free families