MathDBRepresentability conjecture for coordinate q-matroids
Representability conjecture for coordinate q-matroids
A coordinate -matroid is a -matroid whose cyclic flats are spanned by subsets of some linear basis. Its corresponding matroid is the matroid obtained from the coordinate representation by replacing coordinate subspaces with their corresponding subsets of the basis.
Representability conjecture for coordinate q-matroids. If the corresponding matroid of a coordinate -matroid is representable, then the -matroid is representable.
The preceding embedding results establish representability for certain coordinate -matroids, but the conjecture proposes that representability of the corresponding matroid always lifts to the -matroid.
Sources & referencesView supporting material
Primary source
Andrew Fulcher, “A cyclic flat embedding theorem for transversal q-matroids”, arXiv:2603.13550 (2026).
Additional references
4 papers in this index state this conjecture (2011–2026). The statement above is taken from the most recent of them; the others are arXiv:2503.12201, arXiv:1304.6451, arXiv:1105.4163.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.