On sequential growth of trees subject to various labeling constraints: from enumeration to probability theory

Trees, as loop-free graphs, are fundamental hierarchical structures of Nature. Depending on the way their constitutive atoms are labeled, their growth obeys different sequential dynamics when a new atom is being appended to a current tree, possibly forming a new tree. Randomized versions of the underlying counting problems are shown to lead, in general, to Markovian triangular sequences.

کلیدواژه ها:

Combinatorial probability ، distinguishability ، forests ، Markovian‎ ‎triangular sequences ، randomization ، simply generated and increasing trees