PreprintarXiv licencearXiv
Extremal subtrees of critical beta-splitting trees
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.
Related
- The height of discrete-time critical beta-splitting trees
- Jumps and Iterated Jumps of Perfect Subtrees of Positive Trees
- An extremal theorem for non-isomorphic spanning trees
- Extremal Spanning Trees of Random Marked Graphs with Independent Edge Weights
- A Turán-type extremal problem for the number of spanning trees in C4-free graphs
BibTeX
@misc{brandenberger2026extremal,
title = {{Extremal subtrees of critical beta-splitting trees}},
author = {Anna Brandenberger and Byron Chin and Elchanan Mossel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24973},
eprint = {2609.24973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24973},
}
RIS
TY - UNPB
TI - Extremal subtrees of critical beta-splitting trees
AU - Anna Brandenberger
AU - Byron Chin
AU - Elchanan Mossel
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24973
UR - https://arxiv.org/abs/2609.24973
AB - 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.
ER -