Enumeration and limit laws of dissections on a cylinder
We compute the generating function for triangulations on a cylinder, with the restriction that all vertices belong to its boundary and that the intersection of a pair of different faces is either empty, a vertex or an edge. We generalize these results to maps with either constant ({k}-dissections) o...
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| Format: | article |
| Publication Date: | 2010 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/8372 |
| Online Access: | https://hdl.handle.net/2117/8372 https://dx.doi.org/10.1016/j.disc.2010.06.023 |
| Access Level: | Open access |
| Keyword: | Combinatorial analysis Maps Geometric dissections Cylinders Triangulations Anàlisi combinatòria Mapes Cilindres Triangulació Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Summary: | We compute the generating function for triangulations on a cylinder, with the restriction that all vertices belong to its boundary and that the intersection of a pair of different faces is either empty, a vertex or an edge. We generalize these results to maps with either constant ({k}-dissections) or unrestricted (unrestricted dissections) face degree. We apply singularity analysis to the resulting generating functions to obtain asymptotic estimates for their coefficients, as well as limit distributions for natural parameters. |
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