Some properties of crossings and partitions Original Research Article

We give a group theoretical interpretation of the lattice of non-crossing partitions of a cycle of length m. Using this interpretation, we prove that the group of skew-automorphisms of this lattice is isomorphic to the dihedral group D4m. We also give some generating functions, in terms of continued fraction expansions, for some statistics on the set of partitions involving the number of restricted crossings and the number of classes.