The Semi-Meander Model

Abstract

The upper arch involution, midpoint winding and lower rainbow connectivity encode the OEIS semi-meander model.

Upper matchings are fixed-point-free noncrossing involutions on twice n endpoints. The winding counts arches crossing the midpoint once each. The one-loop predicate uses upper pairing steps and the fixed lower rainbow. The corresponding formal definition is presented with the all-order count.