Three applications of coverings to difference patterns
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913467115503616 |
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| author | Karam, Thomas |
| author_facet | Karam, Thomas |
| contents | We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of these statements to distance $2$ versions of the pattern, (ii) reduction of these statements to relative versions, and (iii) reductions of these statements to a quasirandom case with respect to some quantities that affect the number of realisations of the pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three applications of coverings to difference patterns Karam, Thomas Combinatorics Number Theory Probability 05D10 (Primary), 05D05, 05D40 (Secondary) We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of these statements to distance $2$ versions of the pattern, (ii) reduction of these statements to relative versions, and (iii) reductions of these statements to a quasirandom case with respect to some quantities that affect the number of realisations of the pattern. |
| title | Three applications of coverings to difference patterns |
| topic | Combinatorics Number Theory Probability 05D10 (Primary), 05D05, 05D40 (Secondary) |
| url | https://arxiv.org/abs/2408.06812 |