combinatorics / Matroid theory

White's Conjecture on Matroids

White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank $9$ binary matroid constitutes a counterexample.

40Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

combinatoricsJul 2, 2026Significance 40/100Registry: unreviewed

White's Conjecture on Matroids

Prior state unknowndisproved

White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank $9$ binary matroid constitutes a counterexample.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank $9$ binary matroid constitutes a counterexample.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.

White's Conjecture on Matroids — Mathematical Frontier Network