This article is cited in 1 paper

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

Abstract: 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 $|S|\ge M$.

Received: 13.12.2002

Language: English

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