A. Newman

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20152022

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math.AT2020

Topology and geometry of random 2-dimensional hypertrees

Matthew Kahle, Andrew Newman

A hypertree, or $Q$ -acyclic complex, is a higher-dimensional analogue of a tree. We study random $2$ -dimensional hypertrees according to the determinantal measure suggeste…

math.AT2018

A lower bound on the number of homotopy types of simplicial complexes on $n$ vertices

Andrew Newman

For $n \in N$ , let $h (n)$ denote the number of simplicial complexes on $n$ vertices up to homotopy equivalence. Here we prove that $h (n) \geq 2^{2^{0.02 n}}$ when $n$ is la…

Topology and geometry of random 2-dimensional hypertrees

A lower bound on the number of homotopy types of simplicial complexes on n vertices

A lower bound on the number of homotopy types of simplicial complexes on $n$ vertices