Persistent Graphs and Cyclic Polytope Triangulations
نویسندگان
چکیده
We prove a bijection between the triangulations of 3-dimensional cyclic polytope C(n+2, 3) and persistent graphs with n vertices. show that under this Stasheff-Tamari orders on naturally translate to subgraph inclusion graphs. Moreover, we describe connection second higher Bruhat order B(n, 2). additionally give an algorithm efficiently enumerate all vertices thus 3).
منابع مشابه
Persistent Triangulations
Triangulations of a surface are of fundamental importance in computational geometry, engineering simulation, and computer graphics. For example, the convex hull of a set of points may be constructed as a triangulation, and there is a close relationship between Delaunay triangulations and Voronoi diagrams in geometry. Triangulations are ordinarily represented as mutable graph structures for whic...
متن کاملThe Number of Triangulations of the Cyclic Polytope C (n, n-4)
We show that the exact number of triangulations of the cyclic poly-tope C (n; n ? 4) is (n + 4)2 n?4 2 ? n if n is even and 3n+11 2 p 2 2 n?4 2 ? n if n is odd. These formulas were previously conjectured by the second author. Our techniques are based on Gale duality and the concept of virtual chambers. They further provide formulas for the number of triangu-lations which use a speciic simplex. ...
متن کاملLinkages in Polytope Graphs
A graph is k-linked if any k disjoint vertex-pairs can be joined by k disjoint paths. We improve a lower bound on the linkedness of polytopes slightly, which results in exact values for the minimal linkedness of 7-, 10and 13-dimensional polytopes. We analyze in detail linkedness of polytopes on at most (6d + 7)/5 vertices. In that case, a sharp lower bound on minimal linkedness is derived, and ...
متن کاملAmoebas, Monge-ampère Measures, and Triangulations of the Newton Polytope
The amoeba of a holomorphic function f is, by definition, the image in Rn of the zero locus of f under the simple mapping that takes each coordinate to the logarithm of its modulus. The terminology was introduced in the 1990s by the famous (biologist and) mathematician Israel Gelfand and his coauthors Kapranov and Zelevinsky (GKZ). In this paper we study a natural convex potential function N f ...
متن کاملExpansive Motions and the Polytope of Pointed Pseudo-Triangulations
We introduce the polytope of pointed pseudo-triangulations of a point set in the plane, defined as the polytope of infinitesimal expansive motions of the points subject to certain constraints on the increase of their distances. Its 1-skeleton is the graph whose vertices are the pointed pseudo-triangulations of the point set and whose edges are flips of interior pseudo-triangulation edges. For p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Combinatorica
سال: 2021
ISSN: ['0209-9683', '1439-6912']
DOI: https://doi.org/10.1007/s00493-020-4369-5