Dealer's random bits in perfect secret sharing schemes Dealer's random bits in perfect secret sharing schemes

L. Csirmaz:

A triangle inequality for polymatroids

A matroid is a submodular and monotome function f from a lattice L to the non-negative real numbers. The conditional rank, coming from entrophy theory, is defined as f(x|y)=f(xy)-f(y). Finally, we can define the distance of two lattice elements by
           f(x|y)+f(y|x)
  d(x,y) = -------------.
               f(xy)
We show that this satisfies the triangle inequality in all polymatroids.