Integral point sets in higher dimensional affine spaces over finite fields
نویسندگان
چکیده
منابع مشابه
Maximal integral point sets in affine planes over finite fields
Motivated by integral point sets in the Euclidean plane, we consider integral point sets in affine planes over finite fields. An integral point set is a set of points in the affine plane F2q over a finite field Fq, where the formally defined squared Euclidean distance of every pair of points is a square in Fq. It turns out that integral point sets over Fq can also be characterized as affine poi...
متن کاملIntegral point sets over finite fields
We consider point sets in the affine plane Fq where each Euclidean distance of two points is an element of Fq . These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces Em. We determine their maximal cardinality I(Fq , 2). For arbitrary commutative rings R instead of Fq or for further restrictions as no three points on a line or no four points on a...
متن کاملInclusion-maximal integral point sets over finite fields
We consider integral point sets in affine planes over finite fields. Here an integral point set is a set of points in F2q where the formally defined Euclidean distance of every pair of points is an element of Fq. From another point of view we consider point sets over F2q with few and prescribed directions. So this is related to Rédei’s work. Another motivation comes from the field of ordinary i...
متن کاملIntegral Cayley Graphs Generated by Distance Sets in Vector Spaces over Finite Fields
Si Li and the fourth listed author (2008) considered unitary graphs attached to the vector spaces over finite rings using an analogue of the Euclidean distance. These graphs are shown to be integral when the cardinality of the ring is odd or the dimension is even. In this paper, we show that the statement also holds for the remaining case: the cardinality of the ring is even and the dimension i...
متن کاملOn Point Sets in Vector Spaces over Finite Fields That Determine Only Acute Angle Triangles
For three points u, v and w in the n-dimensional space IFq over the finite field IFq of q elements we give a natural interpretation of an acute angle triangle defined by this points. We obtain an upper bound on the size of a set Z such that all triples of distinct points u,v,w ∈ Z define acute angle triangles. A similar question in the real space Rn dates back to P. Erdős and has been studied b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2009
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2009.03.001