Projections in vector spaces over finite fields

Abstract

Abstract. We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional projections via projections of random sets. In the end we study the projections of sets which have the (discrete) Fourier decay.

Threshold functions for substructures in random subsets of finite vector spaces

“…Combining (11) and (12) shows that (10) is vanishing, and together with (9), this completes the proof.…”

Restricted Families of Projections and Random Subspaces

“…Recently there has been a growing interest in studying finite field version of some classical problems arising from Euclidean spaces. In [2], the author studied the projections in vector spaces over finite fields, and obtained the Marstrand-Mattila type projection theorem in this setting. For finite fields version of restricted families of projection, the author [3] obtained that a random collection of subspaces admit a Marstrand-Mattila type theorem with high probability.…”

“…For finite fields version of restricted families of projection, the author [3] obtained that a random collection of subspaces admit a Marstrand-Mattila type theorem with high probability. For more details on finite fields version of projections, and finite fields version of restricted families of projection, we refer to [2] and [3], respectively.…”

Distinct spreads in vector spaces over finite fields

“…Using discrete Fourier analysis, Chen [4] proved the following theorem. He stated his result over prime fields, but it can be extended to arbitrary finite fields using the same method.…”