Growing uniform planar maps face by face
| Autor: | Caraceni, Alessandra, Stauffer, Alexandre |
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| Přispěvatelé: | Caraceni, Alessandra, Stauffer, Alexandre |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Popis: | We provide "growth schemes" for inductively generating uniform random $2p$-angulations of the sphere with $n$ faces, as well as uniform random simple triangulations of the sphere with $2n$ faces. In the case of $2p$-angulations, we provide a way to insert a new face at a random location in a uniform $2p$-angulation with $n$ faces in such a way that the new map is precisely a uniform $2p$-angulation with $n+1$ faces. Similarly, given a uniform simple triangulation of the sphere with $2n$ faces, we describe a way to insert two new adjacent triangles so as to obtain a uniform simple triangulation of the sphere with $2n+2$ faces. The latter is based on a new bijective presentation of simple triangulations that relies on a construction by Poulalhon and Schaeffer. Comment: New version correcting a major typo in a statement |
| Databáze: | OpenAIRE |
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