In this paper we provide a method to obtain tight lower bounds on the minimum
redundancy achievable by a Huffman code when the probability distribution
underlying an alphabet is only partially known. In particular, we address the
case where the occurrence probabilities are unknown for some of the symbols in
an alphabet. Bounds can be obtained for alphabets of a given size, for
alphabets of up to a given size, and for alphabets of arbitrary size. The
method operates on a Computer Algebra System, yielding closed-form numbers for
all results. Finally, we show the potential of the proposed method to shed some
light on the structure of the minimum redundancy achievable by the Huffman
code
