The two parts of this Memoir contain two separate but related papers. The
longer paper in Part A obtains necessary and sufficient conditions for several types
of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the
defining stochastic matrix of each Markov chain by a matrix whose entries are
polynomials with positive coefficients in several variables; a Bernoulli shift is repre-
sented by a single polynomial with positive coefficients, p. This transforms jointly
topological and measure-theoretic coding problems into combinatorial ones. In
solving the combinatorial problems in Part A, we state and make use of facts from
Part B concerning pn and its coefficients.
Part B contains the shorter paper on pn and its coefficients, and is independent
of Part A.
An announcement describing the contents of this Memoir may be found in the
Electronic Research Announcements of the AMS at the following Web address:
Received by the editor February 8, 1999.
The second author was partially supported by NSF Grant DMS-9622866 and also thanks
Erwin Schroedinger Institute, Vienna for their support and hospitality during a visit in the summer
of 1997.
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