Abstract. Let ∆ be a Delzant polytope in Rn and b ∈ Zn. Let E denote the symplectic fibration over S determined by the pair (∆, b). We prove the equivalence between the fact that (∆, b) is a mass linear pair (D. McDuff, S. Tolman, Polytopes with mass linear functions, part I. arXiv:0807.0900 [math.SG]) and the vanishing of a characteristic number of E in the following cases: When ∆ is a ∆n−1 bu...

Given a finite collection P of convex n-polytopes in RP (n ≥ 2), we consider a real projective manifold M which is obtained by gluing together the polytopes in P along their facets in such a way that the union of any two adjacent polytopes sharing a common facet is convex. We prove that the real projective structure on M is 1. convex if P contains no triangular polytope, and 2. properly convex ...

In this paper we consider polytopes given by systems of n inequalities in d variables, where every inequality has at most two variables with nonzero coefficient. We denote this family by LI(2). We show that despite of the easy algebraic structure, polytopes in LI(2) can have high complexity. We construct a polytope in LI(2), whose number of vertices is almost the number of vertices of the dual ...

here‎, ‎we aim to develop a new algorithm for solving a multiobjective linear programming problem‎. ‎the algorithm is to obtain a solution which approximately meets the decision maker's preferences‎. ‎it is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution‎. ‎numerical examples and a simulation study are used to...

A force capacity evaluation for a given posture may provide better understanding of human motor abilities applications in sport sciences, rehabilitation and ergonomics. From data on maximum isometric joint torques, the upper-limb feasible set hand was predicted by four models called ellipsoid, scaled polytope polytope, which were compared with measured polytope. The volume, shape prediction err...

We study how the lift-and-project method introduced by Lovász and Schrijver [SIAM J. Optim., 1 (1991), pp. 166–190] applies to the cut polytope. We show that the cut polytope of a graph can be found in k iterations if there exist k edges whose contraction produces a graph with no K5-minor. Therefore, for a graph G with n ≥ 4 nodes with stability number α(G), n − 4 iterations suffice instead of ...

We show that a minimal triangulation of the associahedron (Stasheff polytope) of dimension n is made of (n+ 1)n−1 simplices. We construct a natural bijection with the set of parking functions from a new interpretation of parking functions in terms of shuffles. Introduction The Stasheff polytope, also known as the associahedron, is a polytope which comes naturally with a poset structure on the s...

This article presents numerical methods in order to solve problems of tolerance analysis. A geometric specification, a contact specification and a functional requirement can be respectively characterized by a finite set of geometric constraints, a finite set of contact constraints and a finite set of functional constraints. Mathematically each constraint formalises a n-face (hyperplan of dimens...

The diameter of a set P of n points in R is the maximum Euclidean distance between any two points in P . If P is the vertex set of a 3-dimensional convex polytope, and if the combinatorial structure of this polytope is given, we prove that, in the worst case, deciding whether the diameter of P is smaller than 1 requires Ω(n log n) time in the algebraic computation tree model. It shows that the ...

The Single Row Facility Layout Problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [Discrete Applied Mathematics 157(1)(2009)183-190]. For any number of departments n, we prove that the ...