29 citations · 72 across the 26 of their papers we have counts for
4 papers · 1 filter
A note on traces of set families
Balazs Patkos
A family of sets is defined to be -trace -Sperner if for any -subset of the family of traces $\mathcal{F}|_L=\{F \cap L: F \in \m…
Two-part set systems
Dániel Gerbner, Péter L. Erdős, Nathan Lemons +3
The two part Sperner theorem of Katona and Kleitman states that if is an -element set with partition , and $\cF$ is a family of subsets of such that no two…
On the ratio of maximum and minimum degree in maximal intersecting families
Zoltán Loránt Nagy, Lale Özkahya, Balázs Patkós +1
To study how balanced or unbalanced a maximal intersecting family is we consider the ratio $\mathcal{R}(\mathcal{F})=\frac{Δ(\mathcal{F})}{δ(\…
Saturating Sperner families
Dániel Gerbner, Balázs Keszegh, Nathan Lemons +3
A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still sat…