S d := {x = (x1, . . . , xd) ∈ R : 0 6 x1, . . . , xd 6 1, 0 6 x1 + · · ·+ xd 6 1} denote the standard simplex in R. We denote by ∂S the boundary of S. We will also use barycentric coordinates on the simplex which we denote by the boldface symbol x = (x0, x1, . . . , xd), x0 := 1−x1−· · ·−xd. We will use standard multiindex notation such as x := x0 0 x α1 1 · · ·xd d and α n := (α0 n , α1 n , ·...
