The Reciprocal of 1+ab+aabb+aaabbb+... for NONCOMMUTING a and b,
Catalan numbers and non commutative quadratic equations
By
Arkady Berenstein, Christophe Reutenauer, Vladimir Retakh and Doron Zeilberger
.pdf
.ps
.tex
[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!) noncommuting. Then
algebra really becomes combinatorics!
Maple Package

NCFPS
handles noncommutative formal power series.
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