Vol. 12, No. 2, 2019

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ISSN: 1944-4184 (e-only)
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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
Abstract

We provide a cyclic permutation analogue of the Erdős–Szekeres theorem. In particular, we show that every cyclic permutation of length (k 1)( 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.

Keywords
cyclic Erdős–Szekeres theorem
Mathematical Subject Classification 2010
Primary: 05D99
Milestones
Received: 7 April 2018
Revised: 9 July 2018
Accepted: 22 July 2018
Published: 8 October 2018

Communicated by Joshua Cooper
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