Ramseyan variations on symmetric subsequences

Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/54

Title:	Ramseyan variations on symmetric subsequences
Authors:	Verbitsky, Oleg
Issue Date:	13-Dec-2002
Publisher:	Луганский национальный университет им. Т. Шевченко
Description:	A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation f : {0, 1, . . . , n} → {0, 1, . . . , 2n} with the restriction f(i + 1) ≤ 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 ⊆ {0, 1, . . . , n} with \|S\| ≥ M.
URI:	http://hdl.handle.net/123456789/54
Appears in Collections:	Статті

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