Add to ORKGThis thesis concerns the cap set problem in affine geometry. The problem is illustrated by the card game SET and its geometrical interpretation in ternary affine space. The maximal cardinality of a cap is known for the dimension one to six. For the four lowest dimensions, a maximal cap is constructed and the optimality of its size proven. From there, two recursive methods are described and applied to obtain upper bounds for the maximal size of caps in dimensions seven to ten. The best found upper bounds are 291, 771, 2070 and 5619, respectively
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. Fo...
This bachelor thesis provides a mathematical description of the card game of SET. The reader is intr...
Abstract. This paper begins by discussing the game SET, and uses it as an introduction to affine cap...
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...
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 this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
A 2-cap in the affine geometry $AG(n, q)$ is a subset of 4 points in general position. In this paper...
In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
We construct large caps in projective spaces of small dimension (up to 11) defined over fields of or...
This bachelor thesis provides a mathematical description of the card game of SET. The reader is intr...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of 픽nq with no ...
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. Fo...
This bachelor thesis provides a mathematical description of the card game of SET. The reader is intr...
Abstract. This paper begins by discussing the game SET, and uses it as an introduction to affine cap...
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...
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 this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
A 2-cap in the affine geometry $AG(n, q)$ is a subset of 4 points in general position. In this paper...
In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the si...
In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a sub...
We construct large caps in projective spaces of small dimension (up to 11) defined over fields of or...
This bachelor thesis provides a mathematical description of the card game of SET. The reader is intr...
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of 픽nq with no ...
AbstractIn this paper we present a general method to construct caps in higher-dimensional projective...
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. Fo...
This bachelor thesis provides a mathematical description of the card game of SET. The reader is intr...