1 5 Se p 20 05 On the number of t - ary trees with a given path length
نویسنده
چکیده
We show that the number of t-ary trees with path length equal to p is exp ( h(t−1)t log t p log p (1 + o(1)) ) , where h(x)=−x log x−(1−x) log(1−x) is the binary entropy function. Besides its intrinsic combinatorial interest, the question recently arose in the context of information theory, where the number of t-ary trees with path length p estimates the number of universal types, or, equivalently, the number of different possible Lempel-Ziv’78 dictionaries for sequences of length p over an alphabet of size t.
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