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math.AT2019★ 4 cited
Weighted Path homology of Weighted Digraphs and Persistence
Yong Lin, Shiquan Ren, Chong Wang +1
In recent years, A. Grigor'yan, Y. Lin, Y. Muranov and S.T. Yau [6, 7, 8, 9] constructed a path homology theory for digraphs. Later, S. Chowdhury and F. Memoli [3] studied the pers…
math.AT2019
Discrete Morse Theory for Weighted Simplicial Complexes
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key diffe…