On the homology of several number-theoretic set families
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914858373480448 |
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| author | Goh, Marcel K. Saks, Jonah |
| author_facet | Goh, Marcel K. Saks, Jonah |
| contents | This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition on a set family that results in easy computation of the homology groups, and show that the first three examples, among many others, admit such a structure. We then extend our techniques to address the complexes associated to coprime-free sets and a generalization of primitive sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12535 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the homology of several number-theoretic set families Goh, Marcel K. Saks, Jonah Combinatorics Algebraic Topology Number Theory 06A07, 11B75 This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition on a set family that results in easy computation of the homology groups, and show that the first three examples, among many others, admit such a structure. We then extend our techniques to address the complexes associated to coprime-free sets and a generalization of primitive sets. |
| title | On the homology of several number-theoretic set families |
| topic | Combinatorics Algebraic Topology Number Theory 06A07, 11B75 |
| url | https://arxiv.org/abs/2206.12535 |