  We consider the concept of irreducible meandric system introduced by Lando
and Zvonkin. We place this concept in the lattice framework of NC(n). As a
consequence, we show that the even generating function for irreducible meandric
systems is the R-transform of XY, where X and Y are classically (commuting)
independent random variables, and each of X,Y has centred semicircular
distribution of variance 1. Following this point of view, we make some
observations about the symmetric linear functional on polynomials which has
R-transform given by the even generating function for meanders.
