Efficient computations of discrete cubical homology
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909621641281536 |
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| author | Kapulkin, Chris Kershaw, Nathan |
| author_facet | Kapulkin, Chris Kershaw, Nathan |
| contents | We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing literature, with the key insights including: a faster way to generate all singular cubes, reducing the dimensions of vector spaces in the chain complex by taking a quotient over automorphisms of the cube, and preprocessing graphs using the axiomatic treatment of discrete cubical homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient computations of discrete cubical homology Kapulkin, Chris Kershaw, Nathan Computational Geometry Algebraic Topology Combinatorics 05-04, 05C25, 55U15 We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing literature, with the key insights including: a faster way to generate all singular cubes, reducing the dimensions of vector spaces in the chain complex by taking a quotient over automorphisms of the cube, and preprocessing graphs using the axiomatic treatment of discrete cubical homology. |
| title | Efficient computations of discrete cubical homology |
| topic | Computational Geometry Algebraic Topology Combinatorics 05-04, 05C25, 55U15 |
| url | https://arxiv.org/abs/2410.09939 |