Persistent Pairs And Connectedness In Discrete Morse Functions On Simplicial Complex I
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910487943315456 |
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| author | Zheng, Chong |
| author_facet | Zheng, Chong |
| contents | In this paper, we study some useful properties of persistent pairs in a discrete Morse function on a simplicial complex $K$. In case of $\dim K=1$ (i.e., a graph), by using the properties, we characterize strongly connectedness of critical simplices between two distinct discrete Morse functions, and relate the number of such pairs to the Euler characteristic of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06922 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Persistent Pairs And Connectedness In Discrete Morse Functions On Simplicial Complex I Zheng, Chong Combinatorics Algebraic Topology In this paper, we study some useful properties of persistent pairs in a discrete Morse function on a simplicial complex $K$. In case of $\dim K=1$ (i.e., a graph), by using the properties, we characterize strongly connectedness of critical simplices between two distinct discrete Morse functions, and relate the number of such pairs to the Euler characteristic of $K$. |
| title | Persistent Pairs And Connectedness In Discrete Morse Functions On Simplicial Complex I |
| topic | Combinatorics Algebraic Topology |
| url | https://arxiv.org/abs/2304.06922 |