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no. 4
Demi-shuffle duals of Magnus polynomials in a free associative algebra
Nakamura, Hiroaki1
1 Osaka University Department of Mathematics, Graduate School of Science Toyonaka, Osaka 560-0043 (Japan)
Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 929-939.

We study two linear bases of the free associative algebra ℤ〈X,Y〉: one is formed by the Magnus polynomials of type (ad X k 1 Y)⋯(ad X k d Y)X k and the other is its dual basis (formed by what we call the “demi-shuffle” polynomials) with respect to the standard pairing on the monomials of ℤ〈X,Y〉. As an application, we derive a formula of Le–Murakami, Furusho type that expresses arbitrary coefficients of a group-like series J∈ℂ〈〈X,Y〉〉 in terms of the “regular” coefficients of J.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.287
Classification: 10X99, 14A12, 11L05
Keywords: shuffle product, non-commutative polynomial, group-like series

Nakamura, Hiroaki 1

1 Osaka University Department of Mathematics, Graduate School of Science Toyonaka, Osaka 560-0043 (Japan)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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. https://alco.centre-mersenne.org/articles/10.5802/alco.287/

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