Minors for alternating dimaps

Understand

We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex.

• We show that they are related by the triality relation of Tutte.
• They do not commute in general, though do in many circumstances, and we characterise the situations where they do.
• The relationship with triality is reminiscent of similar relationships for binary functions, due to the author, so we characterise those alternating dimaps which correspond to binary functions.