163 citations · 327 across the 36 of their papers we have counts for
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math.QA2010★ 4 cited
A short proof of Kontsevich cluster conjecture
Arkady Berenstein, Vladimir Retakh
We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by nonco…
math.RA2010
Hilbert series of algebras associated to direct graphs and order homology
Vladimir Retakh, Shirlei Serconek, Robert Wilson
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necess…
math-ph2010★ 35 cited
Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation
Vladimir Retakh, Vladimir Rubtsov
We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hank…