  We investigate when limits of graphs (graphons) and permutations (permutons)
are uniquely determined by finitely many densities of their substructures,
i.e., when they are finitely forcible. Every permuton can be associated with a
graphon through the notion of permutation graphs. We find permutons that are
finitely forcible but the associated graphons are not. We also show that all
permutons that can be expressed as a finite combination of monotone permutons
and quasirandom permutons are finitely forcible, which is the permuton
counterpart of the result of Lovasz and Sos for graphons.
