论文信息 - Neighborly cubical spheres and a cubical lower bound conjecture

Neighborly cubical spheres and a cubical lower bound conjecture

Using mirrors and cyclic polytopes, we construct cubicald-spheres which are the analogs of cyclic polytopes in the sense that they have the ⌉d−1/2⌈-skeleta of cubes. The existence of these neighborly cubical spheres leads to a special case of an upper bound conjecture for cubical spheres, suggested by Kalai. We extend the same construction to show that the closed convex hull off-vectors of cubical spheres contains a cone described by Adin, as an analog to the generalized lower bound theorem for simplicial polytopes.

Louis J. Billera | L. Billera | E. Babson | Eric K. Babson | Clara S. Chan

[1] Ron M. Adin,et al. A new cubical h-vector , 1996, Discret. Math..

[2] R. Blind,et al. Convex polytopes without triangular faces , 1990 .

[3] William Jockusch. The lower and upper bound problems for cubical polytopes , 1993, Discret. Comput. Geom..

[4] Richard P. Stanley,et al. Generalized $H$-Vectors, Intersection Cohomology of Toric Varieties, and Related Results , 1987 .

[5] H. S. M. Coxeter,et al. Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues , 1938 .

[6] C. Rourke,et al. Introduction to Piecewise-Linear Topology , 1972 .

[7] T. Januszkiewicz,et al. Convex polytopes, Coxeter orbifolds and torus actions , 1991 .

[8] Wolfgang Kühnel,et al. Tight Polyhedral Submanifolds and Tight Triangulations , 1995 .

[9] P. McMullen,et al. A generalized lower-bound conjecture for simplicial polytopes , 1971 .

[10] Michael Davis. Some aspherical manifolds , 1987 .