Demi-Shuffle Duals of Magnus Polynomials in a Free Associative Algebra

Explore a 38-minute conference talk by Hiroaki Nakamura from Osaka University, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the study of two linear bases in free associative algebra: Magnus type polynomials and their dual basis, known as 'demi-shuffle' polynomials. Discover how these concepts are applied to derive a Le-Murakami, Furusho type formula, expressing arbitrary coefficients of a group-like series in terms of its "regular" coefficients. Gain insights into Nakamura's recent paper published in Algebraic Combinatorics, which forms the foundation of this presentation. Enhance your understanding of advanced algebraic concepts and their applications in combinatorics.