| Abstract: | A matroid is sticky if any two of its extensions by disjoint sets can be glued together along the common restriction (that
is, they have an amalgam). The sticky matroid conjecture asserts that a matroid is sticky if and only if it is modular. Poljak
and Turzík proved that no rank-3 matroid having two disjoint lines is sticky. We show that, for r ≥ 3, no rank−r matroid having two disjoint hyperplanes is sticky. These and earlier results show that the sticky matroid conjecture for
finite matroids would follow from a positive resolution of the rank-4 case of a conjecture of Kantor. |
