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pro vyhledávání: '"REN, Shiquan"'
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a91f68ba12549e718c4e9bbf737ae5ef
http://arxiv.org/abs/2108.02384
http://arxiv.org/abs/2108.02384
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5571262eba1fd17900320c5386f32cc2
http://arxiv.org/abs/2103.15870
http://arxiv.org/abs/2103.15870
In this paper, we generalize the embedded homology in \cite{hg1} for hypergraphs and study the relative embedded homology for hypergraph pairs. We study the topology for sub-hypergraphs. Using the relative embedded homology and the topology for sub-h
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed549b64b6924cdd62ab59f7bd9c9281
http://arxiv.org/abs/2102.03967
http://arxiv.org/abs/2102.03967
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 K\"{u}nneth formula of hypergraphs which can be generalized to the K\"{u}nneth formula for the
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https://explore.openaire.eu/search/publication?articleId=arXiv_______::24a7a4fc1f003bccb7d65cfba895d10b
http://arxiv.org/abs/2003.05142
http://arxiv.org/abs/2003.05142
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 K��nneth formula of hypergraphs which can be generalized to the K��nneth formula for th
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https://explore.openaire.eu/search/publication?articleId=doi_________::8d0dcf0f75e72c1ff2d67aa27eb8ab13
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 persistent path homology for directed networks. In this paper, we generali
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8cb73ef4191df58317e94d6586e3dcf6
Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a generalization of the homology of simplicial complexes, the embedded hom
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81f16af647f56cac2518704daa1855d1