Structure of polyzetas and explicit representation on transcendence bases of shuffle and stuffle algebras

DOI10.1016/j.jsc.2016.11.007zbMath1371.16042arXiv1612.06011OpenAlexW2962758593MaRDI QIDQ2628313

Gérard H. E. Duchamp, Van Chien Bui, V. Hoang Ngoc Minh, Vincel Hoang Ngoc Minh

Publication date: 1 June 2017

Published in: Journal of Symbolic Computation, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06011

zbMATH Keywords

shuffle algebraPoincaré-Birkhoff-Witt basistranscendence basisnoncommutative generating seriespolyzetasSchützenberger's factorization

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10) Multiple Dirichlet series and zeta functions and multizeta values (11M32) Connections of Hopf algebras with combinatorics (16T30)

Related Items (4)

Structure of polyzetas and explicit representation on transcendence bases of shuffle and stuffle algebras ⋮ (Pure) transcendence bases in \(\varphi\)-deformed shuffle bialgebras ⋮ On the solutions of the universal differential equation with three regular singularities (on solutions of \(KZ_3)\) ⋮ Computation tool for the q -deformed quasi-shuffle algebras and representations of structure of MZVs

Cites Work

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• On a conjecture by Pierre Cartier about a group of associators
• ARI/GARI, dimorphy and multiple zeta arithmetic: a first evaluation
• The multiple zeta value data mine
• Noncommutative algebra, multiple harmonic sums and applications in discrete probability
• Combinatorial study of colored Hurwitz polyzêtas.
• The multiple zeta value algebra and the stable derivation algebra
• Combinatorial aspects of polylogarithms and Euler-Zagier sums
• Quasi-shuffle products
• Lyndon words, polylogarithms and the Riemann \(\zeta\) function
• Structure of polyzetas and Lyndon words
• On the structure of Hopf algebras
• Structure of polyzetas and explicit representation on transcendence bases of shuffle and stuffle algebras
• Dual bases for noncommutative symmetric and quasi-symmetric functions via monoidal factorization
• Sch\"utzenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product
• Hopf Algebras and Transcendental Numbers
• Computation tool for the q -deformed quasi-shuffle algebras and representations of structure of MZVs
• Derivation and double shuffle relations for multiple zeta values
• On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials
• From the algebras of Riemann polyzetas to the algebra of Hurwitz polyzetas

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