Combinatorics/Algebra
Proof of the Kontsevich non-commutative cluster positivity conjecture
[Démonstration de la conjecture de positivité de Kontsevich pour les graines non commutatives]

Présenté par : the Editorial Board

Rupel, Dylan1
1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 929-932.

Nous étendons le modèle des chemins de Dyck, introduit par Lee–Schiffler, pour donner une preuve de la conjecture de positivité de Kontsevich pour les graines non commutatives à paramètres inégaux.

We extend the Lee–Schiffler Dyck path model to give a proof of the Kontsevich non-commutative cluster positivity conjecture with unequal parameters.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2012.10.034
Rupel, Dylan 1

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA 
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Rupel, Dylan. Proof of the Kontsevich non-commutative cluster positivity conjecture. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 929-932. doi : 10.1016/j.crma.2012.10.034. http://www.numdam.org/articles/10.1016/j.crma.2012.10.034/

[1] Berenstein, A.; Retakh, V. A short proof of Kontsevich cluster conjecture, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011) no. 3–4, pp. 119-122

[2] Berenstein, A.; Zelevinsky, A. Quantum cluster algebras, Adv. Math., Volume 195 (2005) no. 2, pp. 405-455

[3] Di Francesco, P.; Kedem, R. Discrete non-commutative integrability: Proof of a conjecture of M. Kontsevich, Int. Math. Res. Not., Volume 2010 (2010) no. 21, pp. 4042-4063 | DOI

[4] Di Francesco, P.; Kedem, R. Non-commutative integrability, paths and quasi-determinants, Adv. Math., Volume 228 (2011) no. 1, pp. 97-152

[5] Fomin, S.; Zelevinsky, A. Cluster algebras I: Foundations, J. Amer. Math. Soc., Volume 15 (2002) no. 2, pp. 497-529

[6] Lee, K.; Schiffler, R. Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables, 2011 (preprint) | arXiv

[7] Usnich, A. Non-commutative Laurent phenomenon for two variables, 2010 (preprint) | arXiv

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