Entropy of underdetermined sequences under constraints to specifications

Sequences of undetermined symbols are considered. Every such symbol is associated with a set of completely defined symbols, one of which can be used to replace (specify) the former. The specification of an undetermined sequence is the result of replacing all of its symbols by some specifications. We consider the classes of all undetermined sequences which have given length and given frequencies of symbols appearance. The combinatorial entropy of the class is logarithm of the minimum cardinality of a set which contains a specification for each sequence of the class. If some constraints to parameters of specifications are introduced we say about the constrained entropy. The article contains the fairly sharp estimates of the constrained combinatorial entropy.