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seminars:comb:abstract.200212lori

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.

seminars/comb/abstract.200212lori.txt · Last modified: 2020/01/29 14:03 (external edit)

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