5 papers
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…
Complete pivoting growth of butterfly matrices and butterfly Hadamard matrices
John Peca-Medlin
The growth problem in Gaussian elimination (GE) remains a foundational question in numerical analysis and numerical linear algebra. Wilkinson resolved the growth problem in GE with…
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…
Burning rooted graph products
John Peca-Medlin
The burning number of a graph is the minimum number of rounds required to burn all vertices when, at each discrete step, existing fires spread to neighboring vertices an…
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…