Integral homology of random simplicial complexes

DOI10.1007/s00454-017-9938-zzbMath1387.05275arXiv1607.06985OpenAlexW2964342059MaRDI QIDQ1702348

Tomasz Łuczak, Yuval Peled

Publication date: 28 February 2018

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06985

zbMATH Keywords

hitting timerandom simplicial complexintegral homologyhomology shadow

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial aspects of simplicial complexes (05E45)

Related Items (19)

Random Simplicial Complexes: Models and Phenomena ⋮ Homological connectivity in random Čech complexes ⋮ Phase transition in cohomology groups of non-uniform random simplicial complexes ⋮ The integer homology threshold in 𝑌_{𝑑}(𝑛,𝑝) ⋮ Abelian groups from random hypergraphs ⋮ Algebraic and combinatorial expansion in random simplicial complexes ⋮ What Are Higher-Order Networks? ⋮ Sharp threshold for rigidity of random graphs ⋮ A simplified second-order Gaussian Poincaré inequality in discrete setting with applications ⋮ Random Simplicial Complexes: Around the Phase Transition ⋮ Extremal hypercuts and shadows of simplicial complexes ⋮ Freeness of the random fundamental group ⋮ On simple connectivity of random 2-complexes ⋮ Small simplicial complexes with prescribed torsion in homology ⋮ Computing persistent homology with various coefficient fields in a single pass ⋮ Vanishing of cohomology groups of random simplicial complexes ⋮ Quantitative aspects of acyclicity ⋮ Cohen–Lenstra Heuristics for Torsion in Homology of Random Complexes ⋮ Topology of random -dimensional cubical complexes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the phase transition in random simplicial complexes
• Enumeration of \({\mathbb{Q}}\)-acyclic simplicial complexes
• Homological connectivity of random 2-complexes
• The threshold for integer homology in random \(d\)-complexes
• On topological minors in random simplicial complexes
• The fundamental group of random 2-complexes
• Spectral Gaps of Random Graphs and Applications
• A Random Triadic Process
• Inside the critical window for cohomology of random k -complexes
• Homological connectivity of random k -dimensional complexes

This page was built for publication: Integral homology of random simplicial complexes