Zobrazeno 1 - 10
of 160
pro vyhledávání: '"REN, Shiquan"'
Autor:
Ren, Shiquan
In this paper, we study the discrete differential calculus on hypergraphs by using the Kouzul complexes. We define the constrained (co)homology for hypergraphs and give the corresponding Mayer-Vietoris sequences. We prove the functoriality of the May
Externí odkaz:
http://arxiv.org/abs/2310.13449
Autor:
Ren, Shiquan
The notion of independence hypergraphs is introduced to investigate the relations between random hypergraphs and random simplicial complexes [29]. With the help of the differential calculus on discrete sets, the constrained homology of simplicial com
Externí odkaz:
http://arxiv.org/abs/2309.06063
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We generalize the dis
Externí odkaz:
http://arxiv.org/abs/2108.02384
Autor:
Ren, Shiquan
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 foundation for the path-homology theory of digraphs. In this paper, by
Externí odkaz:
http://arxiv.org/abs/2107.09868
Autor:
Ren, Shiquan
Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its vertices in $V$. In this paper, we discuss some differential calculus on $V$. We construct some generalized homology groups of $\mathcal{K}$ by using the differential calculu
Externí odkaz:
http://arxiv.org/abs/2104.01452
Autor:
Ren, Shiquan, Wang, Chong
The theory of path homology for digraphs was developed by Alexander Grigor'yan, Yong Lin, Yuri Muranov, and Shing-Tung Yau. In this paper, we consider the differential algebras on digraphs and define the parametrized homology of digraphs as an analog
Externí odkaz:
http://arxiv.org/abs/2103.15870
Autor:
Ren, Shiquan, Wang, Chong
In 2020, Alexander Grigor'yan, Yong Lin and Shing-Tung Yau [4] introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory. Based on the analytic torsion for digraphs introduced
Externí odkaz:
http://arxiv.org/abs/2103.09552
Autor:
Ren, Shiquan, Wu, Chengyuan
A weighted simplicial complex is a simplicial complex with values (called weights) on the vertices. In this paper, we consider weighted simplicial complexes with $\mathbb{R}^2$-valued weights. We study the weighted homology and the weighted analytic
Externí odkaz:
http://arxiv.org/abs/2103.04252
In this paper, we generalize the embedded homology groups of hypergraphs initially given in [S. Bressan, J. Li, S. Ren, and J. Wu, The embedded homology of hypergraphs and applications, Asian J. Math. 23(3)(2019) 479-500] and study the relative embed
Externí odkaz:
http://arxiv.org/abs/2102.03967
Autor:
Wang, Chong, Ren, Shiquan
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 that the homology of the Morse complex and the path homology are isomor
Externí odkaz:
http://arxiv.org/abs/2007.13425