4 papers
Relative homological algebra of filter modules
Fritz Grimpen
Over an arbitrary ordered set we consider the class of filter modules, i.e. indicator modules of filters in the ordered set. We show that the induced exact structure of filter modu…
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 f…
On minimal flat-injective presentations over local graded rings
Fritz Grimpen, Anastasios Stefanou
Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of -graded modules. We consider them in the setting of local graded…
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…