2 problems

Let $(B_1,\dots,B_k)$ and $(B'_1,\dots,B'_k)$ be compatible sequences of $k$ bases of a rank-$r$ matroid. A cyclic exchange is the simultaneous cyclic transfer of elements among di…

Let $(B_1,\dots,B_k)$ and $(B'_1,\dots,B'_k)$ be sequences of $k$ bases of a matroid. Two sequences are compatible if the union of the $B_i$ as a multiset equals the union of the…