The Fibonacci and Parachute Inequalities for ^ -metrics

d(x, y) = 1 ar y\Y = £ \xt y^ |. 1 j) = \xi xA-^ for all 0 < i < j < n. The family of all metrics d on X which are isometrically £^-embeddable forms a cone: C(X) Cn, called cut cone (or Bamming cone). The cut cone Cn is generated by the cut metrics ds for subsets S of X, where ds(i, j) = 1 if \S n {i, j}| = 1 and ds(i, j) = 0 otherwise. Therefore, a metric d on X is isometrically £i-embeddable if and only if d is the conic hull of cut metrics: