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Simplices over finite fields


Author: Hans Parshall
Journal: Proc. Amer. Math. Soc. 145 (2017), 2323-2334
MSC (2010): Primary 11B30, 05D10, 11T24
DOI: https://doi.org/10.1090/proc/13493
Published electronically: January 25, 2017
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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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Additional Information

Hans Parshall
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

DOI: https://doi.org/10.1090/proc/13493
Received by editor(s): July 20, 2016
Published electronically: January 25, 2017
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2017 American Mathematical Society