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We show that the distribution of the major index over the set of involutionsin S_n that avoid the pattern 321 is given by the q-analogue of the n-thcentral binomial coefficient. The proof consists of a composition of threenon-trivial bijections, one being the Robinson-Schensted correspondence,ultimately mapping those involutions with major index m into partitions of mwhose Young diagram fits inside an n/2 by n/2 box. We also obtain a refinementthat keeps track of the descent set, and we deduce an analogous result for thecomajor index of 123-avoiding involutions.

Descent sets on 321-avoiding involutions and hook decompositions of partitions