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- W4300787411 abstract "A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of fixed genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the case of labelled unicellular maps, which are related to all rooted maps by Marcus and Schaeffer's bijection. This gives an immediate derivation of the asymptotic number of unicellular maps of given genus, and a simple bijective proof of a formula of Lehman and Walsh on the number of triangulations with one vertex. From the labelled case, we deduce an expression of the asymptotic number of maps of genus g with n edges involving the ISE random measure, and an explicit characterization of the limiting profile and radius of random bipartite quadrangulations of genus g in terms of the ISE." @default.
- W4300787411 created "2022-10-04" @default.
- W4300787411 creator A5027585618 @default.
- W4300787411 date "2008-04-03" @default.
- W4300787411 modified "2023-10-18" @default.
- W4300787411 title "The structure of unicellular maps, and a connection between maps of positive genus and planar labelled trees" @default.
- W4300787411 doi "https://doi.org/10.48550/arxiv.0804.0546" @default.
- W4300787411 hasPublicationYear "2008" @default.
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