Structure of Polyzetas and Explicit Representation on Transcendence   Bases of Shuffle and Stuffle Algebras
  Polyzetas, indexed by words, satisfy shuffle and quasi-shuffle identities. In this respect, one can explore the multiplicative and algorithmic (locally finite) properties of their generating series. In this paper, we construct pairs of bases in duality on which polyzetas are established in order to compute local coordinates in the infinite dimensional Lie groups where their non-commutative generating series live. We also propose new algorithms leading to the ideal of polynomial relations, homogeneous in weight, among polyzetas (the graded kernel) and their explicit representation (as data structures) in terms of irreducible elements. 
Van Chien Bui and Gerard H. E. Duchamp and Vincel Hoang Ngoc Minh
math.CO