Ramseyan variations on symmetric subsequences

dc.contributor.author	Verbitsky, Oleg
dc.date.accessioned	2015-10-19T12:46:33Z
dc.date.available	2015-10-19T12:46:33Z
dc.date.issued	2002-12-13
dc.identifier.uri	http://hdl.handle.net/123456789/54
dc.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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Луганский национальный университет им. Т. Шевченко	uk_UA
dc.title	Ramseyan variations on symmetric subsequences	uk_UA
dc.type	Article	uk_UA