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Erdős–Szekeres
theorem for cyclic permutations
Éva Czabarka and Zhiyu Wang
Vol. 12 (2019), No. 2, 351–360
DOI: 10.2140/involve.2019.12.351
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Abstract |
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We provide a cyclic permutation analogue of the Erdős–Szekeres theorem. In particular, we show that every cyclic permutation of length has either an increasing cyclic subpermutation of length or a decreasing cyclic subpermutation of length , and we show that the result is tight. We also characterize all maximum-length cyclic permutations that do not have an increasing cyclic subpermutation of length or a decreasing cyclic subpermutation of length . |
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Keywords
cyclic Erdős–Szekeres theorem
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Mathematical Subject Classification 2010
Primary: 05D99
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Milestones
Received: 7 April 2018
Revised: 9 July 2018
Accepted: 22 July 2018
Published: 8 October 2018
Communicated by Joshua Cooper
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Authors |
| Éva Czabarka | |
| Department of Mathematics University of South Carolina Columbia, SC United States |
Department of Pure and Applied
Mathematics University of Johannesburg Johannesburg South Africa |
| Zhiyu Wang | |
| Department of Mathematics University of South Carolina Columbia, SC United States |
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