# Calssifying the Partitions of the problem Cycle Decomposition of Markov Chains

The book Cycle Representations of Markov Processes solves the problem of Mapping Stochastic Matrices induced from a Markov Chain into Partitions using a $\lambda$-preserving ($\lambda$ is a Lebesgue Measure) transformation of the interval $f_{t} = (x+t) \bmod t$ ( $t$ is the rotational length to be considered is $\frac{1}{n!}$) but don't explain if the partition is a Markov Partition or a Generating Partition. I searched several references looking for this proof but there is nothing written about these partitions. If these particular partitions are Markov, how to prove this fact?

• 1. That first sentence is quite a mouthful. I think it'd be easier to follow if you broke it down into multiple sentences and introduced the notation and concepts you are using, defined the problem, and then stated what your question about that problem is. 2. This sounds like a pure math question to me. Generally, pure math questions aren't suitable here, unless the question explains the connection to computer science and why the question needs to be answered from a CS perspective. Can you edit to include that information, or flag this for mod attention to request migration to Math.SE? – D.W. Aug 14 '16 at 20:51