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math.PR2025
The Horton-Strahler number of butterfly trees
John Peca-Medlin
The Horton-Strahler (HS) number, a classical measure of branching complexity arising in hydrology and register allocation, is studied for butterfly trees, a recursive family of bin…
math.PR2025
Heights of butterfly trees
John Peca-Medlin, Chenyang Zhong
Binary search trees (BSTs) are fundamental data structures whose performance is largely governed by tree height. We introduce a block model for constructing BSTs by embedding inter…
math.PR2025
Pivot probabilities and norm effects in Gaussian elimination for -ensembles
Kenji Gunawan, John Peca-Medlin
We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for random matrix ensembles. For GUE matrices, we resolve a previously reported dis…