94 citations · 124 across the 48 of their papers we have counts for
20 papers · 1 filter
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.,…
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.
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.
On the image of convolutions along an arithmetic progression
Ernie Croot, Chi-Nuo Lee
We consider the question of determining the structure of the set of all -dimensional vectors of the form for $A \subseteq \{1,...…
Few products, many h-fold sums
Albert Bush, Ernie Croot
Improving upon a technique of Croot and Hart, we show that for every , there exists an such that if is sufficiently large and $|A.A| \le |A|^{1+ε…
Order-preserving Freiman isomorphisms
Gagik Amirkhanyan, Albert Bush, Ernie Croot
An order-preserving Freiman 2-isomorphism is a map such that if and only if and if and only if …