Involve: A Journal of Mathematics

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

Erdős–Szekeres theorem for cyclic permutations

Éva Czabarka and Zhiyu Wang

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

cyclic Erdős–Szekeres theorem


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

Export citation


  • M. H. Albert, M. D. Atkinson, D. Nussbaum, J.-R. Sack, and N. Santoro, “On the longest increasing subsequence of a circular list”, Inform. Process. Lett. 101:2 (2007), 55–59.
  • J. Aube, E. L. Stitzinger, S. B. Suanmali, and L. M. Zack, paper in progress, 2007, {
  • A. L. Delcher, S. Kasif, R. D. Fleischmann, J. Paterson, O. White, and S. L. Salzberg, “Alignment of whole genomes”, Nuclear Acids Res. 27:11 (1999), 2369–2376.
  • P. Erdős and G. Szekeres, “A combinatorial problem in geometry”, Compositio Math. 2 (1935), 463–470.
  • J. S. Frame, G. \relax de. B. Robinson, and R. M. Thrall, “The hook graphs of the symmetric groups”, Canadian J. Math. 6 (1954), 316–324.
  • D. E. Knuth, The art of computer programming, III: Sorting and searching, 2nd ed., Addison-Wesley, Reading, MA, 1998.
  • D. Romik, “Permutations with short monotone subsequences”, Adv. in Appl. Math. 37:4 (2006), 501–510.
  • R. P. Stanley, Enumerative combinatorics, II, Cambridge Studies in Advanced Mathematics 62, Cambridge University Press, 1999.