On the homology of several number-theoretic set families
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Bibliographic record
Abstract
This paper describes the homology of various simplicial complexes associated with 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 with coprime-free sets and a generalization of primitive sets.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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