Extremal subtrees of critical beta-splitting trees
Anna Brandenberger, Byron Chin, Elchanan Mossel
Abstract
We determine the most and least likely shapes for an instance of the critical beta-splitting tree via a connection to data compression and Huffman's minimum redundancy codes. This allows us to answer combinatorial questions about the distribution of clades posed by Aldous and Janson, stated as problem 7 in arXiv:2303.02529.
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