Simplices over finite fields

Parshall, Hans

doi:10.1090/proc/13493

Simplices over finite fields
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by Hans Parshall PDF

Proc. Amer. Math. Soc. 145 (2017), 2323-2334 Request permission

Abstract:

We prove that, provided $d > k$, every sufficiently large subset of $\mathbf {F}_q^d$ contains an isometric copy of every $k$-simplex that avoids spanning a nontrivial self-orthogonal subspace. We obtain comparable results for simplices exhibiting self-orthogonal behavior.

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