On sticky matroids (Q1100208)

\textit{S. Poljak} and \textit{D. Turzik} [Discrete Math. 42, 119-123 (1982; Zbl 0491.05020)] call a geometric lattice L on the point set E sticky if for any two extensions \(L_ 1\) and \(L_ 2\) on \(E\cup X_ 1\) and \(E\cup X_ 2\), respectively, there exists a geometric lattice \(\tilde L\) on \(E\cup X_ 1\cup X_ 2\) with \(\tilde L\setminus X_ i=L_{3-i}\) for \(i=1,2\). They conjectured that a lattice is sticky if and only if it is modular, and proved this for rank 3 geometries. The present authors show ``that, in order to prove this conjecture, it is sufficient to prove it only for a quite restricted class of rank 4 geometries (which will hopefully some day turn out to be empty).'' As a simple corollary, they obtain the characterization of sticky uniform matroids [\textit{S. Poljak} and \textit{D. Turzik}, Czech. Math. J. 34(109), 239-246 (1984; Zbl 0553.05029)].