Annals of Combinatorics, 11 (2007), 39-46.

A factorization theorem of characteristic polynomials of convex geometries.

by Masahiro Hachimori and Masataka Nakamura


A convex geometry is a closure system whose closure operator satisfies the anti-exchange property. We show that the characteristic polynomial of a 2-spanning convex geometry $K$ factors over nonnegative integers if the clique complex of the nbc-graph of $K$ is pure and shellable. The result is rather ristrivtive, but new in a sense that it does not belong to any of the categries of so far established factorization theorems of characteristic polynomials.