Problem of the Week
Hilton Memorial Lecture
A sufficient condition for the characteristic polynomial of a geometric lattice to have a complete integral factorization is that the lattice be supersolvable, which means it has a maximal chain of modular elements. (However, supersolvability is not a necessary condition for such a factorization.)
Other than some basic lattice theory, I will not assume prior knowledge of the topics discussed during this talk.
In his 1997 paper “A characterization of supersolvable signed graphs”, Young-Jin Yoon presents necessary and sufficient conditions for the bias matroid of a signed graph to be supersolvable. In his 2001 paper “Supersolvable frame-matroid and graphic-lift lattices”, Zaslavsky does the same for biased graphs, a generalization of signed graphs. I will discuss why the two results are not compatible and will prove parts of the correct theorem.