In the case of vector spaces, what this means is that they proved the conjecture in the case where every ( n вЂ“ 1)-element subset of the given set of n 2 vectors is linearly independent. Geelen and Humphries proved that RotaвЂ™s Basis Conjecture is true for paving matroids. I think it is very promising, and I donвЂ™t think many people have looked at it. I want to start with an idea that I mentioned in my MathOverflow post but not in my previous Polymath Blog post. If you have an idea that does not seem to fit into any of the categories below, please consider that to be an invitation to leave a comment about your idea, not an indication that it is not of interest! Matroids with No Small Circuits Assuming this project continues to gather steam, the plan is to populate the associated Polymath Wiki page with a more comprehensive list of references and statements of partial results. Let me emphasize that the list below is not comprehensive, but is meant only to summarize the comments so far and to throw in a few ideas of my own. The other reason to create a new post is to take stock of where we are and perhaps suggest some ways to go forward. I will just say that if you are in doubt, I recommend posting new comments under this post rather than the old one, but if common sense clearly says that your comment belongs under the old post then you should use common sense. I am also told that sometimes, separate вЂњdiscussionвЂќ and вЂњresearchвЂќ threads are created IвЂ™m not seeing an immediate need for such a separation yet, and so I am not going to state a rule that comments of one type belong under the original post whereas comments of some other type belong under this new post. I am told that it is standard Polymath practice to start a new blog post whenever the number of comments reaches about 100, and we have reached that point, so that is one reason I am writing a second post at this time. There has been enough interest that I think we can formally declare RotaвЂ™s Basis Conjecture to be Polymath 12.

Am i a polymath