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A Note on the Sticky Matroid Conjecture
Joseph E. Bonin
Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA
Annals of Combinatorics 15 (4) pp.619-624 December, 2011
AMS Subject Classification: 05B35, 06C10
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 Turz´ık 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.
Keywords: sticky matroid conjecture, bundle condition, cyclic flat


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