Reference : Once Punctured Disks, Non-Convex Polygons, and Pointihedra
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45386
Once Punctured Disks, Non-Convex Polygons, and Pointihedra
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Parlier, Hugo mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Pournin, Lionel [Univ Paris 13, LIPN, Villetaneuse, France.]
2018
ANNALS OF COMBINATORICS
Springer Basel Ag
22
3
619-640
Yes (verified by ORBilu)
0218-0006
Basel
[en] flip-graphs ; triangulations ; combinatorial moduli spaces
[en] We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once punctured polygons which, in turn, contain all possible geometric flip-graphs of polygons with a marked point as embedded sub-graphs. Our main focus is on the geometric properties of these graphs and how they relate to one another. In particular, we show that the embeddings between them are strongly convex (or, said otherwise, totally geodesic). We find bounds on the diameters of these graphs, sometimes using the strongly convex embeddings and show that the topological flip-graph is Hamiltonian. These graphs relate to different polytopes, namely to type D associahedra and a family of secondary polytopes which we call pointihedra.
http://hdl.handle.net/10993/45386
10.1007/s00026-018-0393-1

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