A theorem on cyclic polytopes
β Scribed by G. C. Shephard
- Book ID
- 112888719
- Publisher
- The Hebrew University Magnes Press
- Year
- 1968
- Tongue
- English
- Weight
- 233 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic d polytope with n vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension nd -3. Moreover, we resolve positively a new special case
The cyclic polytope C (n, d) is the convex hull of any n points on the moment curve {(t, t 2 , . . . , t d ) : we consider the fiber polytope (in the sense of Billera and Sturmfels [6]) associated to the natural projection of cyclic polytopes Ο : C(n, d ) β C(n, d) which 'forgets' the last dd coord
A. Kotzig [5] proved the following theorem (cf. B. Griinbaum [2,3,4]: Every 3-polytope has at least one edge such that the sum of valencies of its end-vertices is ~< 13. In this note we deal with improvements of this statement. Let us review first some of the notations employed: If we are given a p