A necessary and sufficient condition is given that a semicontinuous, nonnegative, concave function on a finite dimensional closed convex set $X$ necessarily be ...

The multiple exchange property for matroid bases is generalized for valuated matroids and M-natural concave set functions. The proof is based on the Fenchel-type duality theorem in discrete convex ...

Barycentric coordinates provide a robust framework for expressing any point within a simplex—typically a triangle or convex polygon—as an affine combination of its vertices. This representation has ...