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An Optimal Medium-Strength Regularity Algorithm For 3-Uniform Hypergraphs, John Theado
An Optimal Medium-Strength Regularity Algorithm For 3-Uniform Hypergraphs, John Theado
USF Tampa Graduate Theses and Dissertations
Szemere´di’s Regularity Lemma [32, 33] is an important tool in combinatorics, with numerous appli- cations in combinatorial number theory, discrete geometry, extremal graph theory, and theoretical computer science.
The Regularity Lemma hinges on the following concepts. Let G = (V, E) be a graph and let ∅ /= X, Y ⊂ V be a pair of disjoint vertex subsets. We define the density of the pair (X, Y ) by dG(X, Y ) = |E[X, Y ]|/(|X||Y |) where E[X, Y ] denotes the …
Boolean Partition Algebras, Joseph Anthony Van Name
Boolean Partition Algebras, Joseph Anthony Van Name
USF Tampa Graduate Theses and Dissertations
A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean
algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces
is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness
of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.