Comptes Rendus
Combinatorics/Algebra
A short proof of Kontsevich's cluster conjecture
[Une courte démonstration d'une conjoncture de Kontsevich]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 119-122.

Nous proposons une démonstration élémentaire d'une conjoncture de Kontsevich qui affirme que l'itération de l'application non-commutative rationnelle Kr:(x,y)(xyx1,(1+yr)x1) est donnée par des polynômes de Laurent non-commutatifs.

We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map Kr:(x,y)(xyx1,(1+yr)x1) are given by noncommutative Laurent polynomials.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.004

Arkady Berenstein 1 ; Vladimir Retakh 2

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA
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Arkady Berenstein; Vladimir Retakh. A short proof of Kontsevich's cluster conjecture. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 119-122. doi : 10.1016/j.crma.2011.01.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.004/

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The authors were supported in part by the NSF grant DMS #0800247.

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