4 citations · 6 across the 5 of their papers we have counts for
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Simplicial-like Identities for The Paths and The Regular Paths on Discrete Sets
Shiquan Ren
Simplicial identities play an important and fundamental role in simplicial homotopy theory. On the other hand, the study of the paths and the regular paths on discrete sets is the…
A Discrete Morse Theory for Digraphs
Chong Wang, Shiquan Ren
Digraphs are generalizations of graphs in which each edge is assigned with a direction or two directions. In this paper, we define discrete Morse functions on digraphs, and prove t…
A Künneth Formula of Hypergraphs
Chong Wang, Shiquan Ren, Jian Liu
In this paper, based on the embedded homology groups of hypergraphs defined in \cite{h1}, we define the product of hypergraphs and prove the corresponding Künneth formula of hyperg…
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…
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…
Weighted Fundamental Group
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to th…