PreprintCC BY 4.0arXiv
The Maximum Diagonal Product of a Stochastic Matrix of Bounded Rank
Abstract
Let A=(aij) be a nonnegative row-stochastic or column-stochastic n× n matrix of rank at most k, where 1≤ k≤ n. Write n=qk+s, where 0≤ s<k. The author conjectured in 2018 that, for every permutation σ of {1,…,n}, ∏i=1n ai,σ(i)≤ q−q(k−s)(q+1)−(q+1)s. We prove this bound and classify all equality cases.
Related
- The Maximum Permanent of a Stochastic Matrix of Bounded Rank
- Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group
- Maximum principle for quasilinear SPDE’s on a bounded domain without regularity assumptions
- Breaking the Spin Degeneracy for Distributions of Off-Diagonal Scattering Matrix Elements in the Case of Symplectic Symmetry
- A note on the injective edge coloring of graphs with bounded maximum degree
BibTeX
@misc{lavi2026maximum,
title = {{The Maximum Diagonal Product of a Stochastic Matrix of Bounded Rank}},
author = {Yair Lavi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01763},
eprint = {2611.01763},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01763},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Maximum Diagonal Product of a Stochastic Matrix of Bounded Rank
AU - Yair Lavi
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01763
UR - https://arxiv.org/abs/2611.01763
AB - Let A=(a_ij) be a nonnegative row-stochastic or column-stochastic n× n matrix of rank at most k, where 1≤ k≤ n. Write n=qk+s, where 0≤ s<k. The author conjectured in 2018 that, for every permutation σ of {1,…,n}, ∏_i=1^n a_i,σ(i)≤ q^−q(k−s)(q+1)^−(q+1)s. We prove this bound and classify all equality cases.
ER -