Combinatorial Maps with Normalized Knot

Dainis Zeps (1)

1 IMCS - Institute of Mathematics and Computer Science

We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot's normalization doesn't affect combinatorial map what concerns its generality. Knot's normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the knot. Knot's normalization may be applied to edge structuring knot too. If both are normalized then one is fully and other partially normalized mutually.

Keywords: graphs on surface; zigzag walk; permutations; combinatorial maps; combinatorial knots

Domains: Combinatorics [math.CO]

Dainis Zeps. Combinatorial Maps with Normalized Knot. 2010. ⟨hal-00525168⟩