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2019 Erdős–Szekeres theorem for cyclic permutations
Éva Czabarka, Zhiyu Wang
Involve 12(2): 351-360 (2019). DOI: 10.2140/involve.2019.12.351

Abstract

We provide a cyclic permutation analogue of the Erdős–Szekeres theorem. In particular, we show that every cyclic permutation of length (k1)(1)+2 has either an increasing cyclic subpermutation of length k+1 or a decreasing cyclic subpermutation of length +1, 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 k+1 or a decreasing cyclic subpermutation of length +1.

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Éva Czabarka. Zhiyu Wang. "Erdős–Szekeres theorem for cyclic permutations." Involve 12 (2) 351 - 360, 2019. https://doi.org/10.2140/involve.2019.12.351

Information

Received: 7 April 2018; Revised: 9 July 2018; Accepted: 22 July 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06980507
MathSciNet: MR3864223
Digital Object Identifier: 10.2140/involve.2019.12.351

Subjects:
Primary: 05D99

Keywords: cyclic Erdős–Szekeres theorem

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2019
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