It is considered an important problem by some members of the structural combinatorics community.
[1] A proof of the conjecture was announced, but not published, in 2014 by Geelen, Gerards, and Whittle.
is a set of points in a vector space defined over a field
, and is minor-minimal with that property, is called an "excluded minor"; a matroid
For representability over the real numbers, there are infinitely many forbidden minors.
[7] There are seven forbidden minors for the matroids representable over GF(4).
[8] They are: This result won the 2003 Fulkerson Prize for its authors Jim Geelen, A. M. H. Gerards, and A.
[10] For GF(5), several forbidden minors on up to 12 elements are known,[11] but it is not known whether the list is complete.
Geoff Whittle announced during a 2013 visit to the UK that he, Jim Geelen, and Bert Gerards had solved Rota's conjecture.
[12] It would take them years to write up their research in its entirety and publish it.
[13][14] An outline of the proof appeared 2014 in the Notices of the American Mathematical Society.
[15] Only one paper by the same authors, related to this conjecture, has subsequently appeared.