An update on a few permanent conjectures

Abstract

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise a few new questions for future study. (†conjectures have been recently settled negatively.)

Keywords

• Bapat-Sunder conjecture
• Chollet conjecture
• Drury conjecture
• Foregger conjecture
• Liang-So- Zhang conjecture
• Lie conjecture
• Marcus conjecture
• Marcus-Minc conjecture
• permanent
• permanent dominance conjecture
• permanent-on-top conjecture
• Schur power matrix