Perfect cones

Cones, lattices and Hilbert bases of circuits and perfect matchings

There have been a number of results and conjectures regarding the cone, the lattice and the integer cone generated by the (real-valued characteristic functions of) circuits in a binary matroid. In all three cases, one easily formulates necessary conditions for a weight vector to belong to the set in question. Families of matroids for which such necessary conditions are suucient have been determ...

Additive stable solutions on perfect cones of cooperative games

On Perfect Cones and Absolute Baire-one Retracts

We introduce perfect cones over topological spaces and study their connection with absolute B1-retracts.

Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs

Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

Indecomposable Cones

We study some relations between a reproducing cone K in a linear space V over a fully ordered field F and the cone I(K) in Hom( V, V) consisting of all operators A such that AK G K. In particular, indecomposable cones are considered.