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math.PR2017
On the Largest Part Size and Its Multiplicity of a Random Integer Partition
Ljuben Mutafchiev
Let be a partition of the positive integer chosen umiformly at random among all such partitions. Let and be the largest part size and its multipli…
math.PR2007
Survival Probabilities for N-ary Subtrees on a Galton-Watson Family Tree
Ljuben Mutafchiev
The family tree of a Galton-Watson branching process may contain N-ary subtrees, i.e. subtrees whose vertices have at least N>0 children. For family trees without infinite N-ary su…
math.PR2006
Number of Complete N-ary Subtrees on Galton-Watson Family Trees
George P. Yanev, Ljuben Mutafchiev
We associate with a Bienayme-Galton-Watson branching process a family tree rooted at the ancestor. For a positive integer N, define a complete N-ary tree to be the family tree of a…