Linear embeddings of random complexes

Andrew Newman

Linear embeddings of random complexes

Combinatorics 2023-10-04 v3 Geometric Topology

Authors: Andrew Newman

Abstract

For $X \sim X(n; 1, n^{-\alpha_1}, n^{-\alpha_2}, ...)$ in the multiparameter random simplicial complex model we establish necessary and sufficient strict inequalities on the $\alpha_i$ 's to linearly embed the complex into $\mathbb{R}^{2d}$ .

Keywords

metric embeddings simplicial complexes matrix algorithms

Cite

@article{arxiv.2212.09576,
  title  = {Linear embeddings of random complexes},
  author = {Andrew Newman},
  journal= {arXiv preprint arXiv:2212.09576},
  year   = {2023}
}

Comments

15 pages. There was an error for the odd-dimensional case in the previous version. This version proves the threshold for embeddability into even dimensions only. Section 2 has also been expanded to include more detail

Linear embeddings of random complexes

Abstract

Keywords

Cite

Comments

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