منابع مشابه
Revlex-initial 0/1-polytopes
We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial sets of 0/1-vectors. Thus for each n ≤ 2, we consider the 0/1-knapsack polytope given by all 0/1-vectors x = (x1, . . . , xd) such that ∑d−1 i=0 xi2 i is at most n. The revlex-initial 0/1-polytopes have remarkable extremal properties. In particular, they have surprisingly low numbers of facets and...
متن کاملRevlex-initial 0/1-polytopes
We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are special knapsack-polytopes. It turns out that they have remarkable extremal properties. In particular, we use these polytopes in order to prove that the minimum numbers gnfac(d, n) of facets and the minimum average degree gavdeg(d, n) of the graph of a d...
متن کاملVolker Kaibel and Rafael Mechtel
We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are special knapsack-polytopes. It turns out that they have remarkable extremal properties. In particular, we use these polytopes in order to prove that the minimum numbers gnfac(d, n) of facets and the minimum average degree gavdeg(d, n) of the graph of a d...
متن کاملToric Ideals of Flow Polytopes
We show that toric ideals of flow polytopes are generated in degree 3. This was conjectured by Diaconis and Eriksson for the special case of the Birkhoff polytope. Our proof uses a hyperplane subdivision method developed by Haase and Paffenholz. It is known that reduced revlex Gröbner bases of the toric ideal of the Birkhoff polytope Bn have at most degree n. We show that this bound is sharp fo...
متن کاملHypercube Related Polytopes
Body centered structures are used as seeds for a variety of structures of rank 3 and higher. Propellane based structures are introduced and their design and topological properties are detailed.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2006
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.07.010