Ramseyan variations on symmetric subsequences
A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation \(f : {\{0,1,\ldots,n\}}\rightarrow {\{0,1,\ldots,2n\}}\) with the restriction \(f(i+1)\le f(i) + 2\) such that for every 5-term arithmetic progression \(P\) its image \(f(P)\)...
Збережено в:
| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1147 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation \(f : {\{0,1,\ldots,n\}}\rightarrow {\{0,1,\ldots,2n\}}\) with the restriction \(f(i+1)\le f(i) + 2\) such that for every 5-term arithmetic progression \(P\) its image \(f(P)\) is not an arithmetic progression. In this paper we consider symmetric sets in place of arithmetic progressions and prove lower and upper bounds for the maximum \(M=M(n)\) such that every \(f\) as above preserves the symmetry of at least one symmetric set \(S\subseteq\{0,1,\ldots,n\}\) with \(|S|\ge M\). |
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