Formule exacte pour les cartes biparties simples
Formule exacte pour les
cartes biparties simples
Eric Fusy (LIX, Ecole Polytechnique)
travail en commun avec Olivier Bernardi (MIT)
Slicings formula
The number of ways to ''slice'' the 2-sphere having boundaries of
fixed even sizes (ni boundaries of size 2i for i in [1..k]) is
[Tutte’62] ‘‘a census of slicings’’:
where
Planar maps
• Planar map: connected planar graph embedded in the plane
• rooted map: a corner in the outer face is distinguished
Bipartite maps
• Bipartite map = all faces have even degree
• Slicings formula
number of rooted bipartited maps with
ni faces of degree 2i for i in [1..k] is
Bipartite maps
• Bipartite map = all faces have even degree
• Slicings formula
number of rooted bipartited maps with
ni faces of degree 2i for i in [1..k] is
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