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math.CO2026
4-cycle-free induced subgraphs of grid graphs
Taiki Aiba, Ernie Croot
The avoidance of induced forests, or induced acyclic subgraphs, in -dimensional grid graphs, or lattice graphs, has been studied in Alon et al. and later in Caragiannis et al.,…
math.CO2024
An inverse theorem for generalized arithmetic progression with mild multiplicative property
Ernie Croot, Junzhe Mao
We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.
math.CO2024
Past and future of the cap set problem
Ernie Croot, Vsevolod F. Lev, Péter Pál Pach
We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.