Á. Magyar

Preprint Sep 2026

Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$

Let $d,K,N\in \mathbb{N}$ with $K\geq 3$ and $d\geq 4K+4$. Let $\Delta\subset \mathbb{Z}^d$ be the vertex set of a nondegenerate $(K-1)$-simplex, and let $A\subseteq[N]^d$ contain no nontrivial similar copy of $\Delta$. We prove that \[ |A|\ll_{\Delta,d} N^d\exp\!\left(-c_{\Delta,d}\sqrt{\log N}\right) \] improving upo...

Andrew Lott, Á. Magyar, N. R. Ponagandla · 0 citations

Preprint Sep 2026

Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$

Let $d,K,N\in \mathbb{N}$ with $K\geq 3$ and $d\geq 4K+4$. Let $\Delta\subset \mathbb{Z}^d$ be the vertex set of a nondegenerate $(K-1)$-simplex, and let $A\subseteq[N]^d$ contain no nontrivial similar copy of $\Delta$. We prove that \[ |A|\ll_{\Delta,d} N^d\exp\!\left(-c_{\Delta,d}\sqrt{\log N}\right) \] improving upo...

Andrew Lott, Á. Magyar, N. R. Ponagandla · 0 citations

Preprint Aug 2026

Simplex--center configurations in dense subsets of Euclidean spaces and the integer lattice

We obtain density Ramsey theorems for configurations consisting of the vertices of a simplex $\Delta_o$ together with their barycenter. We prove that any subset $A\subseteq\mathbb{R}^n$ of positive upper density contains an isometric copy of all sufficiently large dilates of $\Delta_o$ together with its barycenter. As...

Á. Magyar · 0 citations