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...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2003 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154678 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Ramseyan variations on symmetric subsequences / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 111–124. — Бібліогр.: 16 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862574659861479424 |
|---|---|
| author | Verbitsky, O. |
| author_facet | Verbitsky, O. |
| citation_txt | Ramseyan variations on symmetric subsequences / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 111–124. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-26T10:17:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154678 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T10:17:12Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Verbitsky, O. 2019-06-15T17:45:34Z 2019-06-15T17:45:34Z 2003 Ramseyan variations on symmetric subsequences / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 111–124. — Бібліогр.: 16 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/154678 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Ramseyan variations on symmetric subsequences Article published earlier |
| spellingShingle | Ramseyan variations on symmetric subsequences Verbitsky, O. |
| title | Ramseyan variations on symmetric subsequences |
| title_full | Ramseyan variations on symmetric subsequences |
| title_fullStr | Ramseyan variations on symmetric subsequences |
| title_full_unstemmed | Ramseyan variations on symmetric subsequences |
| title_short | Ramseyan variations on symmetric subsequences |
| title_sort | ramseyan variations on symmetric subsequences |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154678 |
| work_keys_str_mv | AT verbitskyo ramseyanvariationsonsymmetricsubsequences |