Matroid packing/covering conjecture

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Let MM and NN be tame matroids on the same ground set EE. A packing for a pair of matroids on a set is a pair of disjoint spanning sets, one for each matroid, and a covering is a pair of independent sets, one in each matroid, whose union is the whole ground set. Matroid packing/covering conjecture. The ground set admits a partition

E=P∪˙QE=P\dot\cup Q

such that (M ⁣↾P,N ⁣↾P)(M\!\restriction_P,N\!\restriction_P) has a packing and (M.Q,N.Q)(M.Q,N.Q) has a covering. The conjecture unifies natural infinite analogues of the Base Packing and Base Covering theorems. The paper introduces it as a conjectural equivalent formulation of the matroid intersection conjecture; the supplied status is unknown, so it remains open in this database.

References

Primary source

Nathan Bowler and Johannes Carmesin, “On the intersection conjecture for infinite trees of matroids”, arXiv:1404.6067 (2014).

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