A composition theory for upward planar orders
Combinatorics
2025-05-22 v2 Discrete Mathematics
Category Theory
Abstract
An upward planar order on an acyclic directed graph is a special linear extension of the edge poset of that satisfies the nesting condition. This order was introduced to combinatorially characterize upward plane graphs and progressive plane graphs (commonly known as plane string diagrams). In this paper, motivated by the theory of graphical calculus for monoidal categories, we establish a composition theory for upward planar orders. The main result is that the composition of upward planar orders is an upward planar order. This theory provides a practical method to calculate the upward planar order of a progressive plane graph or an upward plane graph.
Cite
@article{arxiv.2505.13865,
title = {A composition theory for upward planar orders},
author = {Xue Dong and Xuexing Lu and Yu Ye},
journal= {arXiv preprint arXiv:2505.13865},
year = {2025}
}