A Note on the Sticky Matroid Conjecture - Mathematics > CombinatoricsReport as inadecuate

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Abstract: A matroid is sticky if any two of its extensions by disjoint sets can beglued together along the common restriction that is, they have an amalgam.The sticky matroid conjecture asserts that a matroid is sticky if and only ifit is modular. Poljak and Turzik proved that no rank-3 matroid having twodisjoint lines is sticky. We show that, for r at least 3, no rank-r matroidhaving two disjoint hyperplanes is sticky. These and earlier results show thatthe sticky matroid conjecture for finite matroids would follow from a positiveresolution of the rank-4 case of a conjecture of Kantor.

Author: Joseph E. Bonin

Source: https://arxiv.org/

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