Geodesic
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, Tome 6 (2023) no. 4, pp. 929-939

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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.

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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)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Nakamura, Hiroaki. Demi-shuffle duals of Magnus polynomials in a free associative algebra. Algebraic Combinatorics, Tome 6 (2023) no. 4, pp. 929-939. doi: 10.5802/alco.287

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