Geometric combinatorics in discrete settings

MOspace/Manakin Repository

Breadcrumbs Navigation

Geometric combinatorics in discrete settings

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/15768

[+] show full item record


Title: Geometric combinatorics in discrete settings
Author: Covert, David
Keywords: geometric combinatorics
finite fields
sum-product problem
Date: 2011
Publisher: University of Missouri--Columbia
Abstract: This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog of the Furstenberg-Katznelson-Weiss theorem on triangles in R2. Second, we study volume sets in Fd/q and discuss some applications to sum-product problems. Finally, we study geometric combinatorics in Z/qZ. We generalize a result of Hart and Iosevich [27] which has applications to sum-product problems. Finally, we show that the Zd/q analogue of a sphere with unital radius is qd−1-dimensional.
URI: http://hdl.handle.net/10355/15768
Other Identifiers: CovertD-042011-D5439

This item appears in the following Collection(s)

[+] show full item record