We do not currently know of any synonyms for permuton.
The noun permuton is defined as:
A probability measure Φ on the σ-algebra of Borel sets of the unit square [0,1]2 such that Φ has uniform marginals (that is, Φ ([α, β] × [0,1]) = Φ ([0,1] × [α, β]) = β − α for every 0 ≤ α ≤ β ≤ 1).
