On the volume set of point sets in vector spaces over finite fields

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dc.creatorVinh, Le Anh
dc.date2009-03-13
dc.date.accessioned2026-07-07T12:52:40Z
dc.date.available2026-07-07T12:52:40Z
dc.descriptionWe show that if $\mathcal{E}$ is a subset of the $d$-dimensional vector space over a finite field $\mathbbm{F}_q$ ($d \geq 3$) of cardinality $|\mathcal{E}| \geq (d-1)q^{d - 1}$, then the set of volumes of $d$-dimensional parallelepipeds determined by $\mathcal{E}$ covers $\mathbbm{F}_q$. This bound is sharp up to a factor of $(d-1)$ as taking $\mathcal{E}$ to be a $(d - 1)$-hyperplane through the origin shows.
dc.identifierhttps://arxiv.org/abs/0903.2510
dc.identifierhttp://arxiv.org/abs/0903.2510
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223372
dc.subjectCombinatorics
dc.titleOn the volume set of point sets in vector spaces over finite fields
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