We show for a simple d-polyhedron having n facets and fii-dimensional faces that fi⩾(n−d)(d−1i)+(di) for i = 0,1,...,d−2. These bounds are best possible.We also discuss some refinements of this result for simple polyhedra having specified numbers of bounded and unbounded facets
Abstract Since at least half of the d edges incident to a vertex u of a simple d-polytope P either a...
International audienceThe main task of the paper is to investigate the question of the recognition o...
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd:...
Klee in 1966 proved that every simple d-polyhedron P with v facets has at least v−d+1 vertices. Grün...
The problem of calculating exact lower bounds for the number of $k$-faces of $d$-polytopes with $n$ ...
We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n ha...
AbstractWe prove two new upper bounds on the number of facets that a d -dimensional 0/1-polytope can...
Abstract. We give a lower bound for the number of vertices of a general d-dimensional polytope with ...
This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at ...
Abstract. For any convex polyhedron P ⊂ R3 and for any natural number k, let Fk(P) denote the number...
We give a lower bound for the number of vertices of a general d-dimensional polytope with a given nu...
Let ci(n, d) be the number of i-dimensional faces of a cyclic d-polytope on n vertices. We present a...
AbstractSince at least half of the d edges incident to a vertex v of a simple d-polytope P either al...
For a d-dimensional polytope with v vertices, d + 1 = 0.62d. This confirms a conjecture of Grunbaum,...
AbstractThe numbers of k-dimensional faces, fk≡fk(d), k=−1,0,…,d−1, of a d-dimensional convex polyto...
Abstract Since at least half of the d edges incident to a vertex u of a simple d-polytope P either a...
International audienceThe main task of the paper is to investigate the question of the recognition o...
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd:...
Klee in 1966 proved that every simple d-polyhedron P with v facets has at least v−d+1 vertices. Grün...
The problem of calculating exact lower bounds for the number of $k$-faces of $d$-polytopes with $n$ ...
We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n ha...
AbstractWe prove two new upper bounds on the number of facets that a d -dimensional 0/1-polytope can...
Abstract. We give a lower bound for the number of vertices of a general d-dimensional polytope with ...
This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at ...
Abstract. For any convex polyhedron P ⊂ R3 and for any natural number k, let Fk(P) denote the number...
We give a lower bound for the number of vertices of a general d-dimensional polytope with a given nu...
Let ci(n, d) be the number of i-dimensional faces of a cyclic d-polytope on n vertices. We present a...
AbstractSince at least half of the d edges incident to a vertex v of a simple d-polytope P either al...
For a d-dimensional polytope with v vertices, d + 1 = 0.62d. This confirms a conjecture of Grunbaum,...
AbstractThe numbers of k-dimensional faces, fk≡fk(d), k=−1,0,…,d−1, of a d-dimensional convex polyto...
Abstract Since at least half of the d edges incident to a vertex u of a simple d-polytope P either a...
International audienceThe main task of the paper is to investigate the question of the recognition o...
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd:...
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