Add to ORKGA cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$. In this paper, we provide a new lower bound on the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough $n$, there is always a cap set in $\mathbb{F}_3^n$ of size at least $2.218^n$
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
AbstractLet m2′(3,q) be the largest value of k (k<q2+1) for which there exists a complete k-cap in P...
In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix m...
A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$. In...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of F^n_q with n...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of 픽nq with no ...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
This thesis concerns the cap set problem in affine geometry. The problem is illustrated by the card ...
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. Fo...
The growth rate of tri-colored sum-free sets, Discrete Analysis 2018:12, 10 pp. This paper contribu...
Sumsets as unions of sumsets of subsets, Discrete Analysis 2017:14, 5 pp. In May 2016 there was a r...
An $m$-general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general po...
Presented on October 13, 2016 at the Skiles Building, Georgia Tech.Ernest Croot is a Professor in th...
A lower bound for the size of a complete cap of the polar space H(n,q²) associated to the non-degene...
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
AbstractLet m2′(3,q) be the largest value of k (k<q2+1) for which there exists a complete k-cap in P...
In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix m...
A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$. In...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of F^n_q with n...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of 픽nq with no ...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
This thesis concerns the cap set problem in affine geometry. The problem is illustrated by the card ...
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. Fo...
The growth rate of tri-colored sum-free sets, Discrete Analysis 2018:12, 10 pp. This paper contribu...
Sumsets as unions of sumsets of subsets, Discrete Analysis 2017:14, 5 pp. In May 2016 there was a r...
An $m$-general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general po...
Presented on October 13, 2016 at the Skiles Building, Georgia Tech.Ernest Croot is a Professor in th...
A lower bound for the size of a complete cap of the polar space H(n,q²) associated to the non-degene...
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
AbstractLet m2′(3,q) be the largest value of k (k<q2+1) for which there exists a complete k-cap in P...
In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix m...