On ordered face structures and many-to-one computads

TL;DR

This paper introduces ordered face structures, providing a combinatorial framework that explicitly describes many-to-one computads, analogous to positive face structures for positive-to-one computads.

Contribution

It defines ordered face structures and establishes their role in explicitly characterizing many-to-one computads.

Findings

Ordered face structures are introduced as a new combinatorial concept.

A correspondence between ordered face structures and many-to-one computads is established.

The paper provides an explicit combinatorial description of many-to-one computads.

Abstract

We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of many-to-one computads in terms of ordered face structures.