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, . . . , 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 prog...
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| Datum: | 2003 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2003
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154678 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Ramseyan variations on symmetric subsequences / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 111–124. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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. |
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