scholarly journals On the Size of Kakeya Sets in Finite Vector Spaces

10.37236/3190 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Gohar Kyureghyan ◽  
Peter Müller ◽  
Qi Wang
Keyword(s):  
Finite Field ◽  
Upper Bounds ◽  
Vector Spaces ◽  
Minimum Size ◽  
Finite Vector ◽  
Kakeya Set ◽  
Finite Vector Spaces

For a finite field $\mathbb{F}_q$, a Kakeya set $K$ is a subset of $\mathbb{F}_q^n$ that contains a line in every direction. This paper derives new upper bounds on the minimum size of Kakeya sets when $q$ is even.

scholarly journals Finite Vector Spaces and Certain Lattices

10.37236/1355 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Thomas W. Cusick
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Multiplicative Function ◽  
Integer Lattice ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Vector ◽  
Galois Number ◽  
Finite Vector Spaces

The Galois number $G_n(q)$ is defined to be the number of subspaces of the $n$-dimensional vector space over the finite field $GF(q)$. When $q$ is prime, we prove that $G_n(q)$ is equal to the number $L_n(q)$ of $n$-dimensional mod $q$ lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice ${\bf Z}^n$ and having the property that given any point $P$ in the lattice, all points of ${\bf Z}^n$ which are congruent to $P$ mod $q$ are also in the lattice. For each $n$, we prove that $L_n(q)$ is a multiplicative function of $q$.

scholarly journals On λ-fold partitions of finite vector spaces and duality

2011 ◽  
Vol 311 (4) ◽  
pp. 307-318 ◽  
Author(s):  
S. El-Zanati ◽  
G. Seelinger ◽  
P. Sissokho ◽  
L. Spence ◽  
C. Vanden Eynden
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces

scholarly journals Bijective methods in the theory of finite vector spaces

1984 ◽  
Vol 37 (1) ◽  
pp. 80-84 ◽  
Author(s):  
Albert Nijenhuis ◽  
Anita E Solow ◽  
Herbert S Wilf
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces

Functors on Finite Vector Spaces and Units in Abelian Group Rings

1986 ◽  
Vol 29 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Klaus Hoechsmann
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Elementary Abelian Group ◽  
Vector Spaces ◽  
Group Rings ◽  
Cyclic Subgroups ◽  
Group Of Units ◽  
Finite Vector ◽  
Finite Vector Spaces

AbstractIf A is an elementary abelian group, let (A) denote the group of units, modulo torsion, of the group ring Z[A]. We study (A) by means of the compositewhere C and B run over all cyclic subgroups and factor-groups, respectively. This map, γ, is known to be injective; its index, too, is known. In this paper, we determine the rank of γ tensored (over Z);with various fields. Our main result depends only on the functoriality of

scholarly journals Kinematic formulas for finite vector spaces

1998 ◽  
Vol 179 (1-3) ◽  
pp. 121-132 ◽  
Author(s):  
Daniel A. Klain
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces

scholarly journals Kakeya-type sets in finite vector spaces

2011 ◽  
Vol 34 (3) ◽  
pp. 337-355 ◽  
Author(s):  
Swastik Kopparty ◽  
Vsevolod F. Lev ◽  
Shubhangi Saraf ◽  
Madhu Sudan
Keyword(s):  
Vector Spaces ◽  
Finite Vector ◽  
Finite Vector Spaces ◽  
Type Sets

Some semisymmetric graphs arising from finite vector spaces

2019 ◽  
Vol 19 (11) ◽  
pp. 2050216
Author(s):  
H. Y. Chen ◽  
H. Han ◽  
Z. P. Lu
Keyword(s):  
Finite Fields ◽  
Automorphism Groups ◽  
Bipartite Graphs ◽  
Vector Spaces ◽  
Finite Vector ◽  
Semisymmetric Graphs ◽  
Edge Transitive ◽  
Finite Vector Spaces

A graph is worthy if no two vertices have the same neighborhood. In this paper, we characterize the automorphism groups of unworthy edge-transitive bipartite graphs, and present some worthy semisymmetric graphs arising from vector spaces over finite fields. We also determine the automorphism groups of these graphs.

Sign in / Sign up

Export Citation Format

Share Document