Characterization of Erd\"os matrices by their zero entries
Combinatorics
2026-03-20 v2 Metric Geometry
Abstract
An Erd\"os matrix is a bistochastic matrix whose sum of squares of entries (Frobenius norm squared) equals its maxtrace (maximum of all the -traces for permutations 's). We characterize all Erd\"os by the patterns of their zero entries; showing that each such skeleton has at most one . We present an algorithm to find all Erd\"os matrices, which finds them up to quickly and also size . We further show some presently known RCDS matrices to be Erd\"os.
Cite
@article{arxiv.2512.04766,
title = {Characterization of Erd\"os matrices by their zero entries},
author = {Priyanka Karmakar and Hariram Krishna and Souvik Pal and G. Krishna Teja},
journal= {arXiv preprint arXiv:2512.04766},
year = {2026}
}