Rank one lightly mixing (Q1182818)

Five successively stronger mixing conditions are (1) weakly mixing, (2) mildly mixing, (3) lightly mixing, (4) partially mixing, (5) mixing. Within the category of rank one transformations there are examples having property (i) but not \((i+1)\), for \(i=1,2,3,4\). In this paper the authors demonstrate this (for \(i=3\)) by showing that an example of rank one transformation constructed by Chacón is lightly mixing but not partially mixing. They also show that it is not lightly 2-mixing. This is the only such example (i.e., lightly mixing, but not partially mixing and not lightly 2-mixing) obtained by `` cutting and stacking'' construction. Other such examples are obtained as products of transformations that are partially mixing but not lightly 2-mixing.