Paper Info
Title
On The Number Of Coloured Triangulations Of D-Manifolds
Abstract
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 2(O(n))n(n/6) 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.
Year
DOI
Venue
2021
10.1007/s00454-020-00189-w
DISCRETE & COMPUTATIONAL GEOMETRY
Keywords
DocType
Volume
Triangulated manifolds, Random complexes, Enumeration
Journal
65
Issue
ISSN
Citations 
3
0179-5376
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Guillaume Chapuy17311.25
Guillem Perarnau25113.17