Matsubara-Heo–Telen principal matroid determinant conjecture
For every linear space , determine the factorization of its principal matroid determinant into irreducible polynomial factors, including the multiplicity of each factor. Conjecture of Matsubara–Heo–Telen asserts an explicit formula for these factor multiplicities; the supplied sources do not state that formula.
References
Primary source
Additional references
- Splitting the Matroid Determinant — arXiv — Clara Briand, Leonie Kayser, Julian Weigert
Progress summary
A new paper claims to settle the factorization question, but the claim has not yet been independently checked.
Matsubara, Heo, and Telen introduced the principal matroid determinant and left its factor-multiplicity formula as Conjecture in August 2026. The conjecture concerns the irreducible-component factorization of this determinant.
Known results
- Matsubara, Heo, and Telen (2026): established structural properties including the degree, radical, and Newton polytope, but left the multiplicities conjectural.
- Polar Degrees of Matroids (2026): proved the associated dual-defectiveness criterion and the degree formula for the dual variety, while explicitly leaving the determinant factorization open.
September 2026 claimed factorization
Clara Briand, Leonie Kayser, and Julian Weigert claim a complete factorization into irreducible components, using local multiplicity bounds and étale-local descriptions. This would settle the remaining conjecture, but the retrieved abstract does not state the explicit formula and no independent verification was found.
Current status (as of September 2026): A September 2026 paper claims the remaining factorization conjecture is solved, but its result is unverified; the earlier geometric conjectures are reported as proved.
Solutions 0
No solutions have been posted yet.