The Reciprocal of 1+ab+aabb+aaabbb+... for NON-COMMUTING a and b,
Catalan numbers and non commutative quadratic equations
Arkady Berenstein, Christophe Reutenauer, Vladimir Retakh and Doron Zeilberger
[Appeared in "Noncommutative Birational Geometry,
Representations, and Cluster algebras"
(A. Berenstein and V, Retakh, eds.),
Contemporary Mathematics volume 592, 2013, Amer. Math. Soc.]
First Posted: June 18, 2012; This version: Oct. 26, 2012.
We all know how to find the reciprocal of a formal power series of commuting variables
but things are much more interesting if the variables are (totally!) non-commuting. Then
algebra really becomes combinatorics!
handles non-commutative formal power series.
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