A Closed Formula for the Interleaving Distance of Rectangle Persistence Modules

Batan M. A., Landi C., PAMUK M.

Mediterranean Journal of Mathematics, vol.22, no.4, 2025 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.1007/s00009-025-02856-9
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: bottleneck distance, Interleaving distance, multiparameter persistence module, rectangle persistence module
  • Middle East Technical University Affiliated: Yes

Abstract

We give formulas for calculating the interleaving distance between rectangle persistence modules that depend solely on the geometry of the underlying rectangles. Moreover, we extend our results to calculate the bottleneck distance for rectangle decomposable persistence modules.