We characterize the bipartite stable b-matching polytope in terms of linear constraints. The stable b-matching polytope is the convex hull of the characteristic vectors of stable b-matchings, that is, of stable assignments of a two-sided multiple partner matching model. Our proof uses the comparability theorem of Roth and Sotomayor [13] and follows a similar line as Rothblum did in [14] for the...

This article examines the universal polytope P (of type {5, 3, 5}) whose facets are dodecahedra, and whose vertex figures are hemiicosahedra. The polytope is proven to be finite, and the structure of its group is identified. This information is used to classifiy the quotients of the polytope. A total of 145 quotients are found, including 69 section regular polytopes with the same facets and ver...

An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices. The complexity of our algorithm is linear in the number of vertices of the projected polytope and we show empirically that the performance is significantly be...

A remarkable result of I. Shemer [4] states that the combinatorial structure of a neighbourly 2m-polytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic (2m+ 1)-polytope are cyclic.

For any field F, a polynomial f ∈ F [x1, x2, . . . , xk] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F.We present some results giving new integrally indecomposable classes of polygons. C...

The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a polytope P directed by a linear objective function in general position. Studying these paths has the potential to provide new insight into a long standing problem, that of designing a polynomial-time...

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain. 1991 Mathematics Subject classification: primary 52C07; secondary 11H55 An n-dimensional lattice determines two normal partitions of the ...

Bott-Samelson varieties factor the flag variety G/B into a product of CP’s with a map into G/B. These varieties are mostly studied in the case in which the map into G/B is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to tran...

We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a two-dimensional projection (“shadow”) of such a polytope.

Absact Network loading problems occur in the design of telecommunication networks, in many different settings. The polyhedral structure of this problem is important in developing solution methods for the problem. In this paper we investigate the polytope of the problem restricted to one edge of the network (the edge capacity problem). We describe classes of strong valid inequalities for the edg...