Arithmetic properties related to the shuffle-product

2007/05/24 by Roland Bacher, Bacher, Roland
Computer Science · Mathematics · #11B85 #11E08 #11E76 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B85 #msc:11E08 #msc:11E76 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0705.3632

20 pages, contains experimental data

openalex publication_date 2007/05/24 · arxiv created 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Generalised power series determined by linear recurrence relations
• The mechanics of shuffle products and their siblings
• Extended Shuffle Product for Multiple Zeta Values
• An invitation to formal power series
• The Algebraic Closure of the Power Series Field in Positive Characteristic