Add to ORKGIn this paper we provide new characterizing properties of TDI systems. A corollary is Sturmfels’ theorem relating toric initial ideals generated by square-free monomials to unimodular triangulations. A reformulation of these test-sets to polynomial ideals actually generalizes the existence of square-free monomials to arbitrary TDI systems, providing new relations between integer programming and Gröbner bases of toric ideals. We finally show that stable set polytopes of perfect graphs are characterized by a refined fan that is a triangulation consisting only of unimodular cones, a fact that endows the Weak Perfect Graph Theo-rem with a computationally advantageous geometric feature. Three ways of implementing the results are described and s...
Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of...
Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system frac...
Abstract. Let G be a simple graph on the vertex set {1,..., n}. An algebraic object attached to G is...
15 pagesInternational audienceIn this paper we provide new characterizing properties of TDI systems....
19 pages, 1 figure. A restricted draft concerning an earlier stage of this research has been reporte...
AbstractA linear system Ax ⩽ b (A, b rational) is said to be totally dual integral (TDI) if for any ...
We obtain a necessary and sufficient condition for tournaments to possess a min-max relation on pack...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
AbstractWe prove that each (rational) polyhedron of full dimension is determined by a unique minimal...
We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to in...
A vector is dyadic if each of its entries is a dyadic rational number, i.e. of the form a2k for some...
To integer programming, algebraic approaches using Gröbner bases and standard pairs via toric ideals...
A vector is dyadic if each of its entries is a dyadic rational number, i.e. of the form a2k for some...
Consider a regular triangulation of the convex-hull $P$ of a set $\mathcal A$ of $n$ points in $\mat...
Toric ideals are binomial ideals which represent the algebraic relations of finite sets of power-pro...
Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of...
Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system frac...
Abstract. Let G be a simple graph on the vertex set {1,..., n}. An algebraic object attached to G is...
15 pagesInternational audienceIn this paper we provide new characterizing properties of TDI systems....
19 pages, 1 figure. A restricted draft concerning an earlier stage of this research has been reporte...
AbstractA linear system Ax ⩽ b (A, b rational) is said to be totally dual integral (TDI) if for any ...
We obtain a necessary and sufficient condition for tournaments to possess a min-max relation on pack...
In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree le...
AbstractWe prove that each (rational) polyhedron of full dimension is determined by a unique minimal...
We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to in...
A vector is dyadic if each of its entries is a dyadic rational number, i.e. of the form a2k for some...
To integer programming, algebraic approaches using Gröbner bases and standard pairs via toric ideals...
A vector is dyadic if each of its entries is a dyadic rational number, i.e. of the form a2k for some...
Consider a regular triangulation of the convex-hull $P$ of a set $\mathcal A$ of $n$ points in $\mat...
Toric ideals are binomial ideals which represent the algebraic relations of finite sets of power-pro...
Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of...
Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system frac...
Abstract. Let G be a simple graph on the vertex set {1,..., n}. An algebraic object attached to G is...