Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps
Lopsp-operations are operations on maps that are applied locally and are guaranteed to preserve all the orientation-preserving symmetries of maps. Well-known examples of such operations are dual, ambo, truncation, and leapfrog. They are described by plane 3-coloured triangulations with specific prop...
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Discrete Mathematics & Theoretical Computer Science
2024-11-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | http://dmtcs.episciences.org/13080/pdf |
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| author | Heidi Van den Camp Brendan D. McKay |
| author_facet | Heidi Van den Camp Brendan D. McKay |
| author_sort | Heidi Van den Camp |
| collection | DOAJ |
| description | Lopsp-operations are operations on maps that are applied locally and are guaranteed to preserve all the orientation-preserving symmetries of maps. Well-known examples of such operations are dual, ambo, truncation, and leapfrog. They are described by plane 3-coloured triangulations with specific properties. We developed and implemented a program that can generate all lopsp-operations of a given size by reducing the problem of generating lopsp-operations to generating all plane quadrangulations that are not necessarily simple. We extended the program plantri to generate these quadrangulations. |
| format | Article |
| id | doaj-art-d4fd3847cb9d47c7b5e5ae222a45415f |
| institution | Kabale University |
| issn | 1365-8050 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj-art-d4fd3847cb9d47c7b5e5ae222a45415f2025-08-20T03:42:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502024-11-01vol. 26:3Discrete Algorithms10.46298/dmtcs.1308013080Generating Plane Quadrangulations and Symmetry-preserving Operations on MapsHeidi Van den CampBrendan D. McKayLopsp-operations are operations on maps that are applied locally and are guaranteed to preserve all the orientation-preserving symmetries of maps. Well-known examples of such operations are dual, ambo, truncation, and leapfrog. They are described by plane 3-coloured triangulations with specific properties. We developed and implemented a program that can generate all lopsp-operations of a given size by reducing the problem of generating lopsp-operations to generating all plane quadrangulations that are not necessarily simple. We extended the program plantri to generate these quadrangulations.http://dmtcs.episciences.org/13080/pdfmathematics - combinatorics05c30 |
| spellingShingle | Heidi Van den Camp Brendan D. McKay Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05c30 |
| title | Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps |
| title_full | Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps |
| title_fullStr | Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps |
| title_full_unstemmed | Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps |
| title_short | Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps |
| title_sort | generating plane quadrangulations and symmetry preserving operations on maps |
| topic | mathematics - combinatorics 05c30 |
| url | http://dmtcs.episciences.org/13080/pdf |
| work_keys_str_mv | AT heidivandencamp generatingplanequadrangulationsandsymmetrypreservingoperationsonmaps AT brendandmckay generatingplanequadrangulationsandsymmetrypreservingoperationsonmaps |