Cyclic Orderings of Paving Matroids - McGuinness, Sean (The Electronic Journal of Combinatorics, 2024)
A matroid M of rank r is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically orderable if and only if for all e X E(M), |X|r(X) |E(M)|r(M). In this paper, we verify this conjecture for all paving matroids.