Article (Scientific journals)
Once Punctured Disks, Non-Convex Polygons, and Pointihedra
Parlier, Hugo; Pournin, Lionel
2018In Annals of Combinatorics, 22 (3), p. 619-640
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Keywords :
flip-graphs; triangulations; combinatorial moduli spaces
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Parlier, Hugo ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Pournin, Lionel;  Univ Paris 13, LIPN, Villetaneuse, France.
External co-authors :
yes
Title :
Once Punctured Disks, Non-Convex Polygons, and Pointihedra
Publication date :
2018
Journal title :
Annals of Combinatorics
ISSN :
0218-0006
Publisher :
Springer Basel Ag, Basel, Unknown/unspecified
Volume :
22
Issue :
3
Pages :
619-640
Peer reviewed :
Peer Reviewed verified by ORBi
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