Higher Bruhat orders of types B and C

Abstract

We propose versions of higher Bruhat orders for types B and C. This is based on a theory of higher Bruhat orders of type A and their geometric interpretations (due to Manin-Shekhtman, Voevodskii-Kapranov, and Ziegler), and on our study of the so-called symmetric cubillages of cyclic zonotopes.