Academic Journal
Generalized Sewing Constructions for Polytopes
| العنوان: | Generalized Sewing Constructions for Polytopes |
|---|---|
| المؤلفون: | Carl W. Lee, Matthew M. Menzel |
| المساهمون: | The Pennsylvania State University CiteSeerX Archives |
| المصدر: | http://www.ms.uky.edu/~lee/gensewconst.pdf. |
| سنة النشر: | 2004 |
| المجموعة: | CiteSeerX |
| الوصف: | Two major combinatorial problems are to characterize the f-vectors and flag f-vectors of convex d-polytopes. For 3-polytopes these problems were solved by Steinitz [24, 25] nearly a century ago. They also were solved for the class of simplicial polytopes by Stanley [23] and Billera and Lee [10] more than 25 years ago. For d ≥ 4, however, the problems of characteriz-ing the f-vectors and flag f-vectors of general d-polytopes are unresolved. Several linear and non-linear inequalities for flag f-vectors of d-polytopes have been established, but in order to confirm whether a set of conditions is sufficient for describing the flag f-vectors of d-polytopes it is necessary to develop new methods for constructing classes of nonsimplicial polytopes. This paper will focus on a new technique for constructing d-polytopes, which is a generalization of Shemer’s sewing construction for simplicial neighborly polytopes [22], and which has been modified to allow the construction of nonsimplicial polytopes as well. One motivation for this construction is that the ordinary polytopes of Bisztriczky [11, 13], a nice generalization of cyclic polytopes, can be constructed by generalized sewing. We also will construct several infinite families of polytopes in this manner, including one whose g-vectors satisfy the relation g2 = 0, and we will consider bounds on the flag f-vectors of 4-polytopes that can be inductively constructed when beginning with the 4-simplex. 1 |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.520.947; http://www.ms.uky.edu/~lee/gensewconst.pdf |
| الاتاحة: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.520.947 http://www.ms.uky.edu/~lee/gensewconst.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| رقم الانضمام: | edsbas.ABB03F3B |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |