Cubillages of cyclic zonotopes

Abstract

This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) of cyclic zonotopes. The combinatorial theory of these objects is of interest in its own right and also has a connection to higher Bruhat orders, triangulations of cyclic polytopes, and Tamari-Stasheff posets applied in the study of Kadomtsev--Petviashvily equations, and etc.