The fine structure of 321 avoiding involutions

Abstract

We study the involutions belonging to the class of 321 avoiding permutations. We calculate the algebraic generating functions of the set containing the involutions avoiding 321 and of some of its subsets. Precisely we determine the algebraic generating functions of the involutions that are expansions of 12, of those expansions of 21, of the simple ones and of their expansions. The graphics of the simple involutions are caracterized. Being the simple involutions avoiding 321 counted by Riordan's numbers, a combinatoric interpretation of the results is illustrated through a class of Motzkin paths. Another interpretation is given through Dyck paths.