Markov exchangeability, a generalization of exchangeability that was proposed by de Finetti, requires that a probability on a string of letters be constant on all strings which have the same initial letter and the same transition counts. The set of Markov exchangeable measures forms a convex set. A graph theoretic and an urn interpretation of the extreme points of this convex set is given.
"Urn Models for Markov Exchangeability." Ann. Probab. 12 (1) 223 - 229, February, 1984. https://doi.org/10.1214/aop/1176993385