Convex Polytopes and Enumeration
نویسندگان
چکیده
منابع مشابه
From Polytopes to Enumeration
In the problem session you saw that v-e+f=2 for 3-polytopes. Is something similar true in higher dimensions? Are there other restrictions on the number of faces of each dimension? What is the most number of faces in each dimension if we fix the number of vertices and dimension? The least? What if we fix other numbers of faces in random dimensions? Notice that all of these questions involve coun...
متن کاملConvex Polytopes
The study of convex polytopes in Euclidean space of two and three dimensions is one of the oldest branches of mathematics. Yet many of the more interesting properties of polytopes have been discovered comparatively recently, and are still unknown to the majority of mathematicians. In this paper we shall survey the subject, mentioning some of the most recent results, and stating the more importa...
متن کاملEnumeration of 2-Level Polytopes
A (convex) polytope P is said to be 2-level if for every direction of hyperplanes which is facet-defining for P , the vertices of P can be covered with two hyperplanes of that direction. The study of these polytopes is motivated by questions in combinatorial optimization and communication complexity, among others. In this paper, we present the first algorithm for enumerating all combinatorial t...
متن کاملEnumeration on words, complexes and polytopes
This thesis presents four papers, studying enumerative problems on combinatorial structures. The first paper studies Forman’s discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. The main motivation is the case ...
متن کاملConvex polytopes and linear algebra
This paper defines, for each convex polytope ∆, a family Hw∆ of vector spaces. The definition uses a combination of linear algebra and combinatorics. When what is called exact calculation holds, the dimension hw∆ of Hw∆ is a linear function of the flag vector f∆. It is expected that the Hw∆ are examples, for toric varieties, of the new topological invariants introduced by the author in Local-gl...
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: Advances in Applied Mathematics
سال: 1997
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0505