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arXiv · 2402.10676

Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps

Heidi Van den Camp·Brendan D. McKay
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Abstract

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.

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Heidi Van den Camp, Brendan D. McKay. 2024-11-06. Generating Plane Quadrangulations and Symmetry-preserving Operations on Maps. https://doi.org/10.46298/dmtcs.13080

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