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.
@article{CRMATH_2022__360_G10_1169_0, author = {Maciej Do{\l}\c{e}ga and Jonathan Novak}, title = {Procesi{\textquoteright}s {Conjecture} on the {Formanek-Weingarten} {Function} is {False}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1169--1172}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.391}, language = {en}, }
Maciej Dołȩga; Jonathan Novak. Procesi’s Conjecture on the Formanek-Weingarten Function is False. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1169-1172. doi : 10.5802/crmath.391. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.391/
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