  Complete non-ambiguous trees (CNATs) are combinatorial objects which appear
in various contexts. Recently, Chen and Ohlig studied the notion of leaf
permutation on these objects, and proposed a series of nice conjectures. Most
of them were proved by Selig and Zhu, through a connexion with the abelian
sandpile model. But one conjecture remained open, about the distribution of a
natural statistic named determinant. We prove this conjecture, in a bijective
way.
