From the 1 of 3 linked papers with an AI index.
3 papers
math.AT2026
Inductive construction of path homology chains and the structure of
Matthew Burfitt, Tyrone Cutler
The paper presents an inductive construction of path homology chain modules for directed graphs using upper and lower extensions parametrized by face multigraphs, providing explici…
math.AT2025
Computing singular simplicial homologies of digraphs and quivers
Matthew Burfitt, Jie Wu, Stephen S. -T. Yau +1
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver…
math.AT2024
Inductive construction of path homology chains
Matthew Burfitt, Tyrone Cutler
Path homology plays a central role in digraph topology and GLMY theory more general. Unfortunately, the computation of the path homology of a digraph is a two-step process, and…