A new and unified approach is presented for constructing joint generating functions for quantities of interest associated with pattern formation in binary sequences. The method is based on results on exponential families of Markov chains. The tools we use are not only new for this area; they seem to be the right approach for deriving general explicit distributional results.
"Explicit distributional results in pattern formation." Ann. Appl. Probab. 7 (3) 666 - 678, August 1997. https://doi.org/10.1214/aoap/1034801248