Flag Bicolorings, Pseudo-Orientations, and Double Covers of Maps

TL;DR

This paper explores the concept of flag bicolorings and pseudo-orientations in maps and maniplexes, introducing a doubling method and analyzing their interrelations to deepen understanding of map symmetries.

Contribution

It introduces a new doubling concept and investigates the relationships between flag bicolorings, pseudo-orientations, and orientations in maps and maniplexes.

Findings

Established connections between flag bicolorings and pseudo-orientations.

Introduced a doubling concept for maps and maniplexes.

Analyzed relationships between various orientation concepts.

Abstract

This paper discusses consistent flag bicolorings of maps and maniplexes, in their own right and as generalizations of orientations and pseudo-orientations. Furthermore, a related doubling concept is introduced, and relationships between these ideas are explored.