For an odd integer r>0 and n>r, we introduce a notion of weakly r-separated collections subsets [n]={1,2,…,n}. When r=1, this corresponds to the concept weak separation introduced by Leclerc Zelevinsky. In paper, extending results due Leclerc-Zelevinsky, develop geometric approach establish number nice combinatorial properties maximal (such as exact upper bound on size collections, mutations ru...

Abstract The positive mass theorem in higher dimensions is proved using causality arguments inspired by those of Penrose et al. (a based on the focusing and retardation null geodesics, 1993) $$3+1$$ 3 + 1 dimensions.