Bisingular maps on the torus
type: Item
instance of: scholarly article
title: Bisingular maps on the torus
zbMATH Open document ID: 1119.05057
DOI: 10.1007/BF02831979
author: Yanpei Liu
author: ZhaoXiang Li
published in: Journal of Applied Mathematics and Computing
publication date: 2007-04-05T00:00:00Z
review text: A map is bisingular if each edge is either a loop or an isthmus (incident on both sides with the same face). A loop is called planar if one of the two regions into which it divides the imbedding surface is homeomorphic to a disc; otherwise is called essential. In this paper a functional equation is presented for the generating function for the number of rooted bisingular maps on the sphere with a given number of loops, a given number of ithmuses and a given root-vertex valency. A similar result is obtained for rooted bisingular maps on the torus as a function of four parameters: the number of planar loops, the number of essential loops, the number of isthmuses and the root-vertex valency. Explicit enumeration formulae are deduced in the cases where the root-vertex valency is ignored and there are no essential loops.
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 5140498
zbMATH Keywords: bisingular map
zbMATH Keywords: rooted map
zbMATH Keywords: planar and toroidal map
zbMATH Keywords: enumerating function
reviewed by: Timothy R. S. Walsh
MaRDI profile type: Publication
cites work: The Enumeration of Maps on the Torus and the Projective Plane
cites work: The asymptotic number of rooted maps on a surface
cites work: The number of rooted 2-connected triangular maps on the projective plane
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cites work: Bisingular maps on the sphere and the projective plane
cites work: A Census of Planar Triangulations
cites work: A Census of Slicings
cites work: A Census of Hamiltonian Polygons
cites work: A Census of Planar Maps
cites work: Counting rooted maps by genus. I
full work available at URL: https://doi.org/10.1007/bf02831979
OpenAlex ID: W1989268086
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description: scientific article; zbMATH DE number 5140498