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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…
Hodge Decompositions for Weighted Hypergraphs
Shiquan Ren, Chengyuan Wu, Jie Wu
Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a ge…
A Discrete Morse Theory for Hypergraphs
Shiquan Ren, Chong Wang, Chengyuan Wu +1
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded ho…
Computing the Homology of Hypergraphs
Shiquan Ren, Chengyuan Wu, Stephane Bressan +1
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have be…