A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914810587774976 |
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| author | Adenwalla, Sarosh |
| author_facet | Adenwalla, Sarosh |
| contents | A permutation of the positive integers avoiding monotone arithmetic progressions of length $4$ with odd common difference was constructed in (LeSaulnier and Vijay, 2011). We generalise this result and show that for each $k\geq 1$, there exists a permutation of the positive integers that avoids monotone arithmetic progressions of length $4$ with common difference not divisible by $2^k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09662 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers Adenwalla, Sarosh Combinatorics 11B25 A permutation of the positive integers avoiding monotone arithmetic progressions of length $4$ with odd common difference was constructed in (LeSaulnier and Vijay, 2011). We generalise this result and show that for each $k\geq 1$, there exists a permutation of the positive integers that avoids monotone arithmetic progressions of length $4$ with common difference not divisible by $2^k$. |
| title | A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers |
| topic | Combinatorics 11B25 |
| url | https://arxiv.org/abs/2302.09662 |