Revlex basis encoding

A string recording which $r$-subsets of $\{1,\dots,n\}$ are bases. It has one character for each of the $\binom{n}{r}$ subsets of size $r$, listed in revlex order (compare the largest elements first, then the next largest, and so on): * means the subset is a basis, 0 means it is not.

For $r=2$, $n=4$ the order is $12, 13, 23, 14, 24, 34$, so 0***** is the matroid in which only $\{1,2\}$ fails to be a basis (elements 1 and 2 are parallel).

The id uses the canonical encoding, the minimal one over all relabelings.