A counterexample to the Foregger-Sinkhorn tie-point conjecture
2026-08-13
Research publication
A counterexample to the Foregger-Sinkhorn tie-point conjecture
arXiv preprint
- Original date
- Authors
- Yair Lavi
- Combinatorics
- Matrix theory
- Permanents
- Doubly stochastic matrices
Abstract
The Foregger-Sinkhorn tie-point conjecture asserts that if a nearly decomposable doubly stochastic matrix minimizes the permanent on a face and the permanental cofactor at a prescribed zero is larger than its permanent, then that zero is a tie point. We give a counterexample in dimension eight.