no. 21-22
Combinatorics/Algebra
Proof of the Kontsevich non-commutative cluster positivity conjecture

Presented by: the Editorial Board

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

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

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.

Received:
Accepted:
Published online:
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, Volume 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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