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Creators/Authors contains: "Kahle, Matthew"

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  1. ; (, Journal of Applied and Computational Topology)
    We study the maximal persistence of an Erdős–Rényi random clique complex filtration on n vertices. 
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  2. ; ; (, Discrete Mathematics & Theoretical Computer Science)
    Symmetric edge polytopes are lattice polytopes associated with finite simplegraphs that are of interest in both theory and applications. We investigate thefacet structure of symmetric edge polytopes for various models of randomgraphs. For an Erd\H{o}s-Renyi random graph, we identify a thresholdprobability at which with high probability the symmetric edge polytope sharesmany facet-supporting hyperplanes with that of a complete graph. We alsoinvestigate the relationship between the average local clustering, also knownas the Watts-Strogatz clustering coefficient, and the number of facets forgraphs with either a fixed number of edges or a fixed degree sequence. We usewell-known Markov Chain Monte Carlo sampling methods to generate empiricalevidence that for a fixed degree sequence, higher average local clustering in aconnected graph corresponds to higher facet numbers in the associated symmetricedge polytope. 
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  3. ; ; (, Journal of Applied and Computational Topology)
    null (Ed.)
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