Some combinatorial results on Bernoulli sets and codes
A Bernoulli set is a set X of words over a finite alphabet A such that for any positive Bernoulli distribution pi in A* one has that pi(X) = 1. In the case of a two-letter alphabet A = {a,b} a characterization of finite Bernoulli sets is given in terms of the function x(i,j) counting the number of words of X having i occurrences of the letter a and j occurrences of the letter b. Moreover, we also derive a necessary and sufficient condition on the distribution x(i,j) which characterizes Bernoulli sets which are commutatively equivalent to prefix codes. (C) 2002 Elsevier Science B.V. All rights reserved.
bernoulli sets codes bernoulli distributions commutative equivalence