Locally Restricted Sequential Structures and Runs of a Subcomposition in   Integer Compositions
  We study part sizes of supercritical locally restricted sequential structures. This extends previous results about locally restricted integer compositions and part sizes in smooth supercritical compositional structures. Applications are given for runs of subcompositions. The problems are formulated as enumerating directed walks in sized infinite digraphs and the proofs depend heavily on earlier results by Bender and Canfield about infinite transfer matrices. 
Edward A. Bender and Zhicheng Gao
math.CO