Transfinite mutations in the completed infinity-gon

Baur, K. and Gratz, S. (2018) Transfinite mutations in the completed infinity-gon. Journal of Combinatorial Theory, Series A, 155, pp. 321-359. (doi: 10.1016/j.jcta.2017.11.011)

Abstract

We introduce mutation along infinite admissible sequences for infinitely marked surfaces, that is surfaces with infinitely many marked points on the boundary. We show that mutation along such admissible sequences produces a preorder on the set of triangulations of a fixed infinitely marked surface. We provide a complete classification of the strong mutation equivalence classes of triangulations of the infinity-gon and the completed infinity-gon respectively, where strong mutation equivalence is the equivalence relation induced by this preorder. Finally, we introduce the notion of transfinite mutations in the completed infinity-gon and show that all its triangulations are transfinitely mutation equivalent, that is we can reach any triangulation of the completed infinity-gon from any other triangulation via a transfinite mutation.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gratz, Dr Sira
• Authors: Baur, K., and Gratz, S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Combinatorial Theory, Series A
• Publisher: Elsevier
• ISSN: 0097-3165
• ISSN (Online): 1096-0899
• Published Online: 21 November 2017
• Copyright Holders: Copyright © 2017 Elsevier Inc.
• First Published: First published in Journal of Combinatorial Theory, Series A 155:321-359
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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