Academic Journal
On the number of coloured triangulations of d-manifolds
| العنوان: | On the number of coloured triangulations of d-manifolds |
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| المؤلفون: | Chapuy, G., Perarnau Llobet, Guillem |
| المساهمون: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| سنة النشر: | 2020 |
| المجموعة: | Universitat Politècnica de Catalunya, BarcelonaTech: UPCommons - Global access to UPC knowledge |
| مصطلحات موضوعية: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Combinatorial analysis, Triangulated manifolds, Random complexes, Enumeration, Anàlisi combinatòria |
| الوصف: | This is a post-peer-review, pre-copyedit version of an article published in Discrete and computational geometry. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00454-020-00189-w ; We give superexponential lower and upper bounds on the number of coloured d-dimensional triangulations whose underlying space is an oriented manifold, when the number of simplices goes to infinity and d=3 is fixed. In the special case of dimension 3, the lower and upper bounds match up to exponential factors, and we show that there are 2O(n)nn6 coloured triangulations of 3-manifolds with n tetrahedra. Our results also imply that random coloured triangulations of 3-manifolds have a sublinear number of vertices. The upper bounds apply in particular to coloured d-spheres for which they seem to be the best known bounds in any dimension d=3, even though it is often conjectured that exponential bounds hold in this case. We also ask a related question on regular edge-coloured graphs having the property that each 3-coloured component is planar, which is of independent interest. ; This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. ERC-2016-STG 716083 “CombiTop”). G. Perarnau acknowledges an invitation in Paris funded by the ERC Grant CombiTop, during which this project was advanced. ; Postprint (author's final draft) |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | 17 p.; application/pdf |
| اللغة: | English |
| تدمد: | 0179-5376 |
| Relation: | Chapuy, G.; Perarnau-Llobet, G. On the number of coloured triangulations of d-manifolds. "Discrete and computational geometry", 11 Març 2020, vol. 65, p. 601-617.; http://hdl.handle.net/2117/343834 |
| DOI: | 10.1007/s00454-020-00189-w |
| الاتاحة: | http://hdl.handle.net/2117/343834 https://doi.org/10.1007/s00454-020-00189-w |
| Rights: | Open Access |
| رقم الانضمام: | edsbas.11B03E02 |
| قاعدة البيانات: | BASE |
| تدمد: | 01795376 |
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| DOI: | 10.1007/s00454-020-00189-w |