Sources which maximize the choice of a Huffman coding tree

Abstract

Since the introduction of the Huffman algorithm (Huffman, 1952) for optimum coding of discrete noiseless sources with specific symbol probabilities, certain combinatorial problems have naturally suggested themselves. One of these is the problem of enumerating the distinct binary trees which correspond to the different available codes. The number of topologically distinct trees has been investigated (cf. Franklin and Golomb, 1975) but this is not a good formulation of the problem. The number of coding-distinct trees for n source symbols is more properly defined as the number of solutions of the Kraft-McMillan Equality, in the form