Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables

DOI10.1016/S0304-3975(00)00445-XzbMath1014.68126OpenAlexW1987152438MaRDI QIDQ1605342

M. Bigotte, Michel Petitot, Nour Eddine Oussous, Gérard Jacob

Publication date: 15 July 2002

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-3975(00)00445-x

zbMATH Keywords

Gröbner basisLyndon wordsquasi-symmetric functionshuffle algebracoloured multiple zeta values functioncoloured polylogarithm function

Mathematics Subject Classification ID

Combinatorics on words (68R15) Symmetric functions and generalizations (05E05) Polylogarithms and relations with (K)-theory (11G55) Numerical approximation and evaluation of special functions (33F05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items

Higher Mahler measure of an $n$-variable family ⋮ Algebraic relations between harmonic sums and associated quantities. ⋮ On harmonic numbers and nonlinear Euler sums ⋮ On Witten multiple zeta-functions associated with semisimple Lie algebras. I ⋮ The multiple zeta value data mine ⋮ Dirichlet type extensions of Euler sums ⋮ Explicit formulas of Euler sums via multiple zeta values ⋮ Computations about formal multiple zeta spaces defined by binary extended double shuffle relations ⋮ Explicit formulas of some mixed Euler sums via alternating multiple zeta values ⋮ Alternating multizeta values in positive characteristic ⋮ A new method for obtaining polylogarithmic Mahler measure formulas ⋮ Explicit formulas of sums involving harmonic numbers and Stirling numbers ⋮ Evaluations of Euler-type sums of weight \(\le 5\) ⋮ Harmonic sums and polylogarithms generated by cyclotomic polynomials

Uses Software

• Maple

Cites Work

• Combinatorial aspects of multiple zeta values
• A natural ring basis for the shuffle algebra and an application to group schemes
• Multiple polylogarithms, cyclotomy and modular complexes
• Evaluations of \(k\)-fold Euler/Zagier sums: a compendium of results for arbitrary \(k\)
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Quasi-shuffle products
• Lyndon Words, Free Algebras and Shuffles
• Algebras of Iterated Path Integrals and Fundamental Groups
• Free differential calculus. IV: The quotient groups of the lower central series
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