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

Free probability aspect of irreducible meander systems, and some related observations about meanders