Demi-shuffle duals of Magnus polynomials in a free associative algebra
Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023
We study two linear bases of the free associative algebra: one is formed by the Magnus type polynomials and the other is its dual basis (formed by what we call the ‘demi-shuffle’ polynomials) with respect to a standard pairing. As an application, we show a formula of Le-Murakami, Furusho type that expresses arbitrary coefficients of a group-like series in terms of its “regular” coefficients. This talk illustrates my recent paper published in Algebraic Combinatorics Volume 6 (2023) no. 4, pp. 929-939.
