Abstract For E ⊂\mathbb F_q^ d, d ≥ 2, where\mathbb F_q is the finite field with q elements,
we consider the distance graph\mathcal G^ dist _t (E), t ≠ 0, where the vertices are the …

A Furstenberg–Katznelson–Weiss type theorem on (d+1)-point configurations in sets of positive
density in finite field geometries - ScienceDirect Skip to main contentSkip to article Elsevier logo …

Let 𝔽 q be a finite field of q elements, where q is a large odd prime power and Q= a 1⁢ x 1 c
1+⋯+ ad⁢ xdcd∈ 𝔽 q⁢[x 1,…, xd], where 2≤ ci≤ N, gcd⁡(ci, q)= 1, and ai∈ 𝔽 q for all 1≤ …

Additive Combinatorics over Finite Fields: New Results and Applications. Page 245 Igor E.
Shparlinski Additive Combinatorics over Finite Fields: New Results and Applications Abstract …

In this paper, we generalize [6],[1],[5] and [3] by allowing the distance between two points in
a finite field vector space to be defined by a general non-degenerate bilinear form or …

For three points, and in the n-dimensional space 𝔽nq over the finite field 𝔽q of q elements
we give a natural interpretation of an acute angle triangle defined by these points. We obtain …

arXiv:0804.4894v1 [math.CO] 30 Apr 2008 Page 1 arXiv:0804.4894v1 [math.CO] 30 Apr 2008
An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density …

On k-simplexes in (2k − 1)-dimensional vector spaces over finite fields Page 1 FPSAC 2009,
Hagenberg, Austria DMTCS proc. AK, 2009, 871–880 On k-simplexes in (2k − 1)-dimensional …

The Number of Occurrences of a Fixed Spread among n Directions in Vector Spaces over Finite
Fields Page 1 Graphs and Combinatorics (2013) 29:1943–1949 DOI 10.1007/s00373-012-1242-3 …

In an earlier paper, for 'large'(but otherwise unspecified) subsets,,, of q, Sárközy showed the
solvability of the equations a+ b= cd with a∈, b∈, c∈, d∈. This equation has been studied …