Random close pack crystal lattices have maximum densities equal to this upper limit. Random close packing does not have a precise geometric definition. It is defined statistically, and results are empirical. A container is randomly filled with objects, and then the container is shaken or tapped until the objects do not compact any further, at this point the packing state is RCP. The definition of packing fraction can be given as: "the volume taken by number of particles in a given space of volume". In other words, packing fraction defines the packing density. It has been shown that the filling fraction increases with
Packing in a hypergraph at time formula_21. For a fixed broodtree, let formula_107 denote the probability that the branching process yields broodtree formula_57. Then the probability that History does not abort is formula_107. By the finiteness of the branching process, formula_110, the summation over all broodtrees formula_57 and History does not abort. The formula_112 distribution of its broodtree approaches the branching process distribution. Thus formula_60. In 1985, Rödl proved Paul Erdős’s conjecture by a method called the Rödl nibble. Rödl's result can be formulated in form of either packing or covering problem. For formula_114 the covering number denoted by formula_115 shows the minimal size