Baur, K orcid.org/0000-0002-7665-476X and Martin, PP (2018) The fibres of the Scott map on polygon tilings are the flip equivalence classes. Monatschefte fur Mathematik, 187 (3). pp. 385-424. ISSN 0026-9255
Abstract
We define a map from tilings of surfaces with marked points to strand diagrams, generalising Scott’s construction for the case of triangulations of polygons. We thus obtain a map from tilings of surfaces to permutations of the marked points on boundary components, the Scott map. In the disk case (polygon tilings) we prove that the fibres of the Scott map are the flip equivalence classes. The result allows us to consider the size of the image as a generalisation of a classical combinatorial problem. We hence determine the size in low ranks.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Tile enumerations; Flip equivalence; Strand diagrams; Plabic graphs |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Aug 2019 14:22 |
Last Modified: | 14 Aug 2019 14:22 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00605-018-1209-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149725 |
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