  Centrosymmetric involutions in the symmetric group S_{2n} are permutations
\pi such that \pi=\pi^{-1} and \pi(i)+\pi(2n+1-i)=2n+1 for all i, and they are
in bijection with involutions of the hyperoctahedral group. We describe the
distribution of some natural descent statistics on 321-avoiding centrosymmetric
involutions, including the number of descents in the first half of the
involution, and the sum of the positions of these descents. Our results are
based on two new bijections, one between centrosymmetric involutions in S_{2n}
and subsets of {1,...,n}, and another one showing that certain statistics on
Young diagrams that fit inside a rectangle are equidistributed. We also use the
latter bijection to refine a known result stating that the distribution of the
major index on 321-avoiding involutions is given by the q-analogue of the
central binomial coefficients.
