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Covering Sets for Rectangles in the Lattice: A Variation on a Classic Combinatorial Problem

Covering Sets for Rectangles in the Lattice: A Variation on a Classic Combinatorial Problem

dc.contributor.advisor Nicholson, Neil
dc.contributor.author Noland, William
dc.contributor.editor Ruthig, Gregory
dc.date.accessioned 2018-01-17T15:27:35Z
dc.date.available 2018-01-17T15:27:35Z
dc.date.issued 2016-11-07
dc.date.submitted 2016-11-07
dc.identifier.uri http://hdl.handle.net/10969/1207
dc.description.abstract This research investigates the minimal covering density for rectangles in the lattice; that is, the smallest possible density of a set of points including at least one corner of every rectangle of a particular size in the lattice (z x z). After determining the covering density for general a x b rectangles is 1/4, we consider pairs of rectangle sizes. We see the density for both a x b and b x a rectangles is the same as for just a x b rectangles. We also prove the minimal density for 1 x 1 and 2 x 2 squares is 1/3. A lemma regarding the integers enables us to find the covering density for a x b and a x d rectangles. Finally, the previous result leads to progress on the most general question: determining the covering density for arbitrary a x b and c x d rectangle pairs. en_US
dc.language.iso en_US en_US
dc.title Covering Sets for Rectangles in the Lattice: A Variation on a Classic Combinatorial Problem en_US
dc.type Thesis

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