A Note on the Sticky Matroid Conjecture

作者：Bonin Joseph E^*

来源：Annals of Combinatorics, 2011, 15(4): 619-624.

DOI：10.1007/s00026-011-0112-7

• sticky matroid conjecture
• bundle condition
• cyclic flat

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 Turzik proved that no rank-3 matroid having two disjoint lines is sticky. We show that, for r a parts per thousand yen 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.

• 出版日期2011-10