14 citations · 49 across the 14 of their papers we have counts for
16 papers
Relative Koszul coresolutions and relative Betti numbers
Hideto Asashiba
Let be a finitely generated right -module for a finite-dimensional algebra over a filed , and the additive closure of . We will define a $\mathca…
Approximation by interval-decomposables and interval resolutions of persistence modules
Hideto Asashiba, Emerson G. Escolar, Ken Nakashima +1
In topological data analysis, two-parameter persistence can be studied using the representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of type…
Characterizations of standard derived equivalences of diagrams of dg categories and their gluings
Hideto Asashiba, Shengyong Pan
A diagram consisting of differential graded (dg for short) categories and dg functors is formulated in this paper as a colax functor from a small category to the 2-category…
On Approximation of D Persistence Modules by Interval-decomposables
Hideto Asashiba, Emerson G. Escolar, Ken Nakashima +1
In this work, we propose a new invariant for D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the ra…
Simplicial complexes and tilting theory for Brauer tree algebras
Hideto Asashiba, Yuya Mizuno, Ken Nakashima
We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the simplicial complexes as lattice polytopes. Via…
On Interval Decomposability of 2D Persistence Modules
Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar +2
In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the cla…