no. G10
Algèbre
Procesi’s Conjecture on the Formanek-Weingarten Function is False
Dołȩga, Maciej1 ; Novak, Jonathan2 
1 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland
2 Department of Mathematics, University of California, San Diego, USA
Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1169-1172.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.391
Dołȩga, Maciej 1 ; Novak, Jonathan 2

1 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland
2 Department of Mathematics, University of California, San Diego, USA 
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Dołȩga, Maciej; Novak, Jonathan. Procesi’s Conjecture on the Formanek-Weingarten Function is False. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1169-1172. doi : 10.5802/crmath.391. http://archive.numdam.org/articles/10.5802/crmath.391/

[1] Biane, Philippe Parking functions of types A and B, Electron. J. Comb., Volume 9 (2002) no. 1, N7, 5 pages | MR | Zbl

[2] Collins, Benît; Matsumoto, Sho; Novak, Jonathan The Weingarten calculus (2021) (https://arxiv.org/abs/2109.14890, to be pusblished in Not. Amer. Math. Soc.)

[3] Matsumoto, Sho; Novak, Jonathan Jucys–Murphy elements and unitary matrix integrals, Int. Math. Res. Not., Volume 2013 (2013) no. 2, pp. 362-397 | DOI | MR | Zbl

[4] Novak, Jonathan Jucys-Murphy elements and the Weingarten function, Noncommutative harmonic analysis with applications to probability. II: Papers presented at the 11th workshop, Bȩdlewo, Poland, August 17–23, 2008 (Banach Center Publications), Volume 89, Polish Academy of Sciences, 2010, pp. 231-235 | DOI | MR | Zbl

[5] Procesi, Claudio A note on the Formanek Weingarten function, Note Mat., Volume 41 (2021) no. 1, pp. 69-110 | MR | Zbl

[6] Stanley, Richard P. Parking functions and noncrossing partitions, Electron. J. Comb., Volume 4 (1997) no. 2, R20, 14 pages | MR | Zbl

[7] Stanley, Richard P. Enumerative Combinatorics. Volume 2, Cambridge Studies in Advanced Mathematics, 62, Cambridge University Press, 1999 | DOI | Zbl

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