Ferroni’s real-rootedness conjecture
For every matroid , the Ehrhart -polynomial of its matroid base polytope has only real zeros.
References
Primary source
Additional references
- Real-rootedness and ultra log-concavity of rank-two matroid Ehrhart h*-polynomials — arXiv — Houshan Fu
Progress summary
A September 2026 preprint claims to disprove universal real-rootedness for matroid Ehrhart polynomials while proving a weaker coefficient property in rank two.
Ferroni’s real-rootedness conjecture asserts universal real-rootedness for the relevant matroid Ehrhart -polynomials. A new preprint claims explicit counterexamples, so the conjecture would be false, while retaining a weaker form of coefficient regularity.
September 2026 counterexamples and weaker theorem
Houshan Fu’s preprint Real-rootedness and ultra log-concavity of rank-two matroid Ehrhart -polynomials claims explicit counterexamples to universal real-rootedness and establishes ultra-log-concavity in the stated ranks. This is a direct claimed disproof, but the preprint is unrefereed.
Current status (as of September 2026): The conjecture is claimed disproved by explicit counterexamples, and a weaker ultra-log-concavity statement is claimed in rank two; both claims await independent verification.
Solutions 0
No solutions have been posted yet.