Veselin Manojlovi\'c, Armaan Ahmed, Yannick Viossat, Robert Noble: Expected and minimal values of a universal tree balance index https://arxiv.org/abs/2507.08615 https://arxiv.org/pdf/2507.08615 https://arxiv.org/html/2507.08615

New preprint! Let me tell you a story about trees, caterpillars, brooms, entropy, and getting scooped by 50 years. Rooted trees of all shapes and sizes crop up all over biology, computing and elsewhere. How can we best compare the shapes of these myriad trees? 1/14 arxiv.org/abs/2507.08615