I'm seeking a widely used notation for "the basis of S". Something like b(S). I'm dealing with I'm dealing with bases of matroids and I want to say things like b(J1) ⊆ b(J2) where J1 and J2 are the independence sets of matroids M1 and M2. b(J1) = basis of J1, b(J2) = basis of J2.

Does anyone know of a widely used convention for "labeling" a basis like this?

Hi chat! any ideas on the above question would be much helpful!

@BAYMAX Is your question about whether or not the determinants always have different sign, or whether or not the determinants are both always negative (under the specified conditions)?

I would like to add a polite rant about the downvotes (two downvotes in thirty minutes) that I got in my recent post with identifier 428251 and title Examples of well-known unsolved problems, in subjects don't related to number theory, that have several equivalent formulations . The only feedback was a comment which I don't agree (with all respect) because I think that I need to ask on a site like MathOverflow to get an answer. Best day for all professors and users.

And I add that this kind of questions that I'm asking on MathOverflow are interesting and important. I am surprised because of the downvotes for these questions.

@user250478 I clicked on your profile but it just lead to your Physics.SE page with no easy way to get to your MO profile. Therefore, to find your question I would need to copy and paste that "identifier" which is a bit tedious.

So I'm not sure how to give my input about why people downvoted the post, nor am I able to upvote it :)