Procesi's Conjecture on the Formanek-Weingarten Function is False. (arXiv:2203.08714v3 [math.CO] UPDATED)

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.

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