Description |
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Abstract: The survival number of a metric space is a newly created statistic.
For a given space, it equals the minimum amount of convex regions necessary to bound
another convex region. Survival number is initially defined in terms of tessellations but
can also be defined as a covering property. In this dissertation, we examine simple,
connected graphs equipped with the path metric and finitely ... read moregenerated groups equipped with
word metrics. We show the survival number of $\mathbb{Z}^2$, depending on the generating
set, equals 3 or 4; and we then equate finding the survival number of $\mathbb{Z}^d$ for
any $d \geq 2$ with an open problem in combinatorial geometry. Last, we compute survival
numbers of Diestel-Leader graphs and lamplighter groups.
Thesis (Ph.D.)--Tufts University, 2015.
Submitted to the Dept. of Mathematics.
Advisor: Moon Duchin.
Committee: Moon Duchin, Larry Guth, Mauricio Gutierez, and Kim
Ruane.
Keyword: Mathematics.read less
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