Procesi's Conjecture on the Formanek-Weingarten Function is False


In this paper, we disprove a recent monotonicity conjecture of C. Procesi on the generating function for monotone walks on the symmetric group, an object which is equivalent to the Weingarten function of the unitary group.

C. R. Math. Acad. Sci. Paris, 360, 1169-1172, 2022