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cs.CG2025
Apex Representatives
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Given a zigzag filtration, we want to find its barcode representatives, i.e., a compatible choice of bases for the homology groups that diagonalize the linear maps in the zigzag. T…
cs.CG2024
Computing Betti tables and minimal presentations of zero-dimensional persistent homology
Yuan Luo, Dmitriy Morozov, Luis Scoccola
The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathem…
cs.CG2024
A Fast Algorithm for Computing Zigzag Representatives
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtr…