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Demi-shuffle duals of Magnus polynomials in a free associative algebra

By Hiroaki Nakamura

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.

Information about the video

  • Date of recording 11/16/23
  • Date of publication 11/22/23
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4



  • Nakamura, Hiroaki. Demi-shuffle duals of Magnus polynomials in a free associative algebra. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 929-939. doi:10.5802/alco.287

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