Annals of Combinatorics, 11 (2007), 39-46.
## A factorization theorem of characteristic polynomials of convex geometries.

by Masahiro Hachimori and Masataka Nakamura

## Abstract

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.