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Jérémie Bettinelli

École polytechnique
Laboratoire d'informatique (LIX)
91128 Palaiseau Cedex
FRANCE
E-mail: firstname « . » lastname « at » normalesup « . » org
Office: 2023
Phone: (+33) (0)1 77 57 80 61
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Plane maps

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In this page, we look at uniform plane maps (maps drawn on the sphere). There is a classical correspondence (sometimes called the trivial bijection) between maps with n edges and quadrangulations (maps whose faces have degree 4) with n faces. To go from quadrangulations to maps, for each face, simply add a vertex in its middle and add four edges linking it to the vertices of the face, then remove the original edges.

It is believed that, in the limit, the map and the quadrangulation should look the same. We show here some examples of uniformly sampled maps with their corresponding quadrangulations (which are hence also uniformly sampled).

Map 30k [jpg1jpg2pdf1pdf23D pdfu3d&tex]   Quad 30k [jpg1jpg2pdf1pdf23D pdfu3d&tex]
Map 50k [jpg1jpg2pdf1pdf23D pdfu3d&tex]   Quad 50k [jpg1jpg2pdf1pdf23D pdfu3d&tex]

Uniform plane maps with 30 000 edges and 50 000 edges, together with the corresponding quadrangulations

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