Publication : t22/009
On quasi-polynomials counting planar tight maps
Bouttier J. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)Guitter E. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Miermont G. (ENS de Lyon, UMPA, CNRS UMR 5669, 46 allée d’Italie, 69364 Lyon Cedex 07, France)
Abstract:Année de publication : 2022
A tight map is a map with some of its vertices marked, such that every vertex of degree 1 is marked. We give an explicit formula for the number N0,n(d1,…,dn) of planar tight maps with n labeled faces of prescribed degrees d1,…,dn, where a marked vertex is seen as a face of degree 0. It is a quasi-polynomial in (d1,…,dn), as shown previously by Norbury. Our derivation is bijective and based on the slice decomposition of planar maps. In the non-bipartite case, we also rely on enumeration results for two-type forests. We discuss the connection with the enumeration of non necessarily tight maps. In particular, we provide a generalization of Tutte's classical slicings formula to all non-bipartite maps.
Preprint : arXiv:2203.14796
Langue : Anglais
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