3 papers
math.AC2026
Relative Gröbner bases of modules and applications in persistence theory
Fritz Grimpen, Matthias Orth, Anastasios Stefanou
Finitely generated modules over the polynomial ring in indeterminates are isomorphic to quotients of finite rank free modules. We introduce a theory of relative Gröbner bases…
math.AT2026
On the Hausdorff stability of barcodes over posets
Mujtaba Ali, Tom Needham, Anastasios Stefanou +1
The Isometry Theorem of Chazal et al. and Lesnick is a fundamental result in persistence theory, which states that the interleaving distance between two one-parameter persistence m…
math.AT2025
Cofiltrations of spanning trees in multiparameter persistent homology
Fritz Grimpen, Anastasios Stefanou
Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID…