Counting Markov Types
نویسندگان
چکیده
The method of types is one of the most popular techniques in information theory and combinatorics. Two sequences of equal length have the same type if they have identical empirical distributions. In this paper, we focus on Markov types, that is, sequences generated by a Markov source (of order one). We note that sequences having the same Markov type share the same so called balanced frequency matrix that counts the number of distinct pairs of symbols. We enumerate the number of Markov types for sequences of length n over an alphabet of size m. This turns out to be asymptotically equivalent to the number of the balanced frequency matrices as well as with the number of special linear diophantine equations, and also balanced directed multigraphs. For fixed m we prove that the number of Markov types is asymptotically equal to
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