# Cubillages of cyclic zonotopes

## TL;DR

This paper surveys recent and past results on cubillages of cyclic zonotopes, highlighting their combinatorial properties and connections to higher Bruhat orders, triangulations, and algebraic structures.

## Contribution

It provides a comprehensive overview of the combinatorial theory of cubillages of cyclic zonotopes, including new insights and connections to other mathematical objects.

## Key findings

- Connections to higher Bruhat orders and triangulations
- Insights into the combinatorial structure of cubillages
- Relevance to algebraic and geometric applications

## 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.