Pré-Publication, Document De Travail Année : 2007

Arithmetic properties related to the shuffle-product

Roland Bacher

Résumé

Properties of the shuffle product suggest the definition of a quadratic form with domain and values in formal power series over a field of characteristic 2. This quadratic form preserves rational (respectively algebraic) power series and its restriction to the affine subspace of series with constant term 1 is bijective. Conjecturally, this bijection restricts to a bijection of rational (respectively algebraic) formal power series.

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Dates et versions

hal-00149241 , version 1 (24-05-2007)
hal-00149241 , version 2 (07-06-2007)

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Roland Bacher. Arithmetic properties related to the shuffle-product. 2007. ⟨hal-00149241v2⟩

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