On torsion in eulerian magnitude homology of Erdos-Renyi random graphs

2024/09/05 by Menara, Giuliamaria
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.03472

Abstract

In this paper we investigate the regimes where an Erdos-Renyi random graph has torsion free eulerian magnitude homology groups. To this end, we start be introducing the eulerian Asao-Izumihara complex - a quotient CW-complex whose homology groups are isomorphic to direct summands of the graph eulerian magnitude homology group. We then proceed by producing a vanishing threshold for a shelling of eulerian Asao-Izumihara complex. This will lead to a result establishing the regimes where eulerian magnitude homology of Erdos-Renyi random graphs is torsion free.

Related

• Eulerian magnitude homology: subgraph structure and random graphs
• Torsion in Magnitude homology theories
• Torsion in the Magnitude homology of graphs
• Cohen--Lenstra heuristics for torsion in homology of random complexes
• Girth, magnitude homology, and phase transition of diagonality