Limit distribution of the number of pairs in generalised allocation scheme
Yu. L. Pavlov, E. V. Cherepanova · Discrete Mathematics and Applications · 2002
Abstract We consider three combinatorial problems covered by generalised allocation scheme: sampling of balls from an urn that contains balls of various colours; random forests; and random permutations with given number of cycles. For these problems, we present limit distributions of the number of pairs of balls of the same colour; of the number of paths in a forest; and of the number of simple (non-closed) paths in the permutation graph respectively. This research was supported by the Russian Foundation for Basic Research, grant 00-01-00233.