Note on islands in path-length sequences of binary trees
  An earlier characterization of topologically ordered (lexicographic) path-length sequences of binary trees is reformulated in terms of an integrality condition on a scaled Kraft sum of certain subsequences (full segments, or islands). The scaled Kraft sum is seen to count the set of ancestors at a certain level of a set of topologically consecutive leaves is a binary tree. 
S. Cortes Reina, S. Foldes, Y. Mardoukhi, N.M. Singhi
math.CO