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 that the achievable packing by the Rödl nibble is in some sense close to that of the random greedy algorithm. The problem of finding the number of such subsets in a "k"-uniform hypergraph was originally motivated through a conjecture by Paul Erdős and Haim Hanani in 1963. Vojtěch Rödl proved their conjecture asymptotically under certain conditions in 1985. Pippenger and Joel Spencer generalized Rödl's results using a random greedy algorithm in 1989. In the following definitions, the hypergraph is denoted by "H"=("V","E"). "H" is called a "k"-uniform hypergraph if every edge in "E" consists of exactly "k" vertices. formula_1 is