104 citations · 132 across the 9 of their papers we have counts for
4 papers · 1 filter
The largest projective cube-free subsets of
Jason Long, Adam Zsolt Wagner
In the Boolean lattice, Sperner's, Erdős's, Kleitman's and Samotij's theorems state that families that do not contain many chains must have a very specific layered structure. We sh…
Nearly-linear monotone paths in edge-ordered graphs
Matija Bucic, Matthew Kwan, Alexey Pokrovskiy +3
How long a monotone path can one always find in any edge-ordering of the complete graph ? This appealing question was first asked by Chvátal and Komlós in 1971, and has since…
Partition problems in high dimensional boxes
Matija Bucic, Bernard Lidicky, Jason Long +1
Alon, Bohman, Holzman and Kleitman proved that any partition of a -dimensional discrete box into proper sub-boxes must consist of at least sub-boxes. Recently, Leader, Mil…
Monochromatic Hilbert cubes and arithmetic progressions
József Balogh, Mikhail Lavrov, George Shakan +1
The Van der Waerden number denotes the smallest such that whenever is --colored there exists a monochromatic arithmetic progression of length . Similarly,…