## Involve: A Journal of Mathematics

• Involve
• Volume 12, Number 2 (2019), 351-360.

### Erdős–Szekeres theorem for cyclic permutations

#### Abstract

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

#### Article information

Source
Involve, Volume 12, Number 2 (2019), 351-360.

Dates
Revised: 9 July 2018
Accepted: 22 July 2018
First available in Project Euclid: 25 October 2018

https://projecteuclid.org/euclid.involve/1540432925

Digital Object Identifier
doi:10.2140/involve.2019.12.351

Mathematical Reviews number (MathSciNet)
MR3864223

Zentralblatt MATH identifier
06980507

Subjects
Primary: 05D99: None of the above, but in this section

Keywords
cyclic Erdős–Szekeres theorem

#### Citation

Czabarka, Éva; Wang, Zhiyu. Erdős–Szekeres theorem for cyclic permutations. Involve 12 (2019), no. 2, 351--360. doi:10.2140/involve.2019.12.351. https://projecteuclid.org/euclid.involve/1540432925

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