On approximation of 2D persistence modules by interval-decomposables

• DOI: 10.1016/j.jaca.2023.100007
• Publication Date: 2023-08-24T16:27:51Z
• Authors: Hideto Asashiba; Emerson G. Escolar; Ken Nakashima; Michio Yoshiwaki
• Keywords: Multiplicity (mathematics); Rank (graph theory)

In this work, we propose a new invariant for 2D persistence modules called the compressed multiplicity and show that it generalizes notions of dimension vector rank invariant. addition, module M, an "interval-decomposable replacement" δ⁎(M) (in split Grothendieck group category modules), which is expressed by pair interval-decomposable modules, is, its positive negative parts. We M if only equal to in group. Furthermore, even not necessarily interval-decomposable, preserves M. provide algorithm compute (a high-level general case, detailed size 2×n case).