Web worlds, web-colouring matrices, and web-mixing matrices

Understand

We introduce a new combinatorial object called a web world that consists of a set of web diagrams.

• The diagrams of a web world are generalizations of graphs, and each is built on the same underlying graph.
• Instead of ordinary vertices the diagrams have pegs, and edges incident to a peg have different heights on the peg.
• The web world of a web diagram is the set of all web diagrams that result from permuting the order in which endpoints of edges appear on a peg.