Combinatorial point configurations and polytopes

Abstract

The monograph is dedicated to exploring combinatorial point configurations derived from mapping a set of combinatorial configurations into Euclidean space. Various methods for this mapping, along with the typology and properties of the resultant configurations, are presented. In addition, the study revolves around combinatorial polytopes defined as convex hulls of combinatorial point configurations. The primary focus lies in examining multipermutation and partial multipermutation point configurations alongside their associated combinatorial polytopes known as multipermutohedra and partial multipermutohedra. Our theoretical contributions are substantiated through the proof of theorems and supporting auxiliary statements. Examples and illustrations are included to enhance the comprehension of the material.