In this correspondence, we prove that the probability distribution induced on the leaves of a Tunstall parse tree for a given source is a (unique) lower bound in the partially ordered set of the probability distributions induced by all possible parse trees with a same number of leaves, and ordered according to the majorization partial order. We apply this result to the problem of optimally approximating a uniform distribution with flips of a biased coin
['Ferdinando Cicalese', 'Luisa Gargano', 'Ugo Vaccaro']
A Note on Approximation of Uniform Distributions From Variable-to-Fixed Length Codes