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Proceedings of the American Mathematical Society

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The unavoidable arrangements of pseudocircles


Authors: Carolina Medina, Jorge Ramírez-Alfonsín and Gelasio Salazar
Journal: Proc. Amer. Math. Soc. 147 (2019), 3165-3175
MSC (2010): Primary 52C30; Secondary 05C10, 52C40
DOI: https://doi.org/10.1090/proc/14450
Published electronically: March 26, 2019
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Abstract: A fact closely related to the classical Erdős-Szekeres theorem is that cyclic arrangements are the only unavoidable simple arrangements of pseudolines: for each fixed $ m\ge 1$, every sufficiently large simple arrangement of pseudolines has a cyclic subarrangement of size $ m$. In the same spirit, we show that there are three unavoidable arrangements of pseudocircles.


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Additional Information

Carolina Medina
Affiliation: Department of Mathematics, University of California, Davis, California 95616
Email: carolitomedina@gmail.com

Jorge Ramírez-Alfonsín
Affiliation: IMAG, Université de Montpellier, CNRS, Montpellier, France; and Unité Mixte Internationale CNRS-CONACYT-UNAM “Laboratoire Solomon Lefschetz”, Cuernavaca, Mexico
Email: jorge.ramirez-alfonsin@umontpellier.fr

Gelasio Salazar
Affiliation: Instituto de Física, Universidad Autónoma de San Luis Potosí, Mexico; and Unité Mixte Internationale CNRS-CONACYT-UNAM “Laboratoire Solomon Lefschetz”, Cuernavaca, Mexico
Email: gsalazar@ifisica.uaslp.mx

DOI: https://doi.org/10.1090/proc/14450
Received by editor(s): August 18, 2018
Received by editor(s) in revised form: October 19, 2018
Published electronically: March 26, 2019
Additional Notes: The first author was supported by Fordecyt grant 265667.
The second author was partially supported by PICS07848 grant and by Program MATH-AMSUD 41327ZL - FLaNASAGraTA
The third author was supported by Conacyt grant 222667 and by FRC-UASLP
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2019 American Mathematical Society