The Reciprocal of ${\sum }_{n\ge 0}{a}^n{b}^n$ for non-commuting $a$ and $b$, Catalan numbers and non-commutative quadratic equations

Arkady Berenstein, Vladimir Retakh, Christophe Reutenauer +1

The aim of this paper is to describe the inversion of the sum ${\sum }_{n\ge 0}{a}^n{b}^n$ where $a$ and $b$ are non-commuting variables as a formal series in $a$ and $b$. We show that t…