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Algebra and Discrete Mathematics, 2003, выпуск 1, страницы 111–124
(Mi adm374)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
Ramseyan variations on symmetric subsequences
Oleg Verbitsky Department of Algebra, Faculty of Mechanics and Mathematics,
Kyiv National University, Volodymyrska 60, 01033 Kyiv, Ukraine
Аннотация:
A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation $f:\{0,1,\dots,n\}\to\{0,1,\dots,2n\}$ 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 $S\subseteq\{0,1,\dots,n\}$ with $|S|\ge M$.
Поступила в редакцию: 13.12.2002
Образец цитирования:
Oleg Verbitsky, “Ramseyan variations on symmetric subsequences”, Algebra Discrete Math., 2003, no. 1, 111–124
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm374 https://www.mathnet.ru/rus/adm/y2003/i1/p111
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Страница аннотации: | 123 | PDF полного текста: | 45 | Первая страница: | 1 |
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