@article{LAMECHE19991,
    title = {Inverse for the shuffle for algebraic series},
    journal = {Applied Mathematics and Computation},
    volume = {98},
    number = {1},
    pages = {1-27},
    year = {1999},
    issn = {0096-3003},
    doi = {https://doi.org/10.1016/S0096-3003(97)10059-5},
    url = {https://www.sciencedirect.com/science/article/pii/S0096300397100595},
    author = {Khira Lameche},
    abstract = {Let K be a commutative field of characteristic 0, and a an algebraic series of one variable with coefficients in K, which is invertible for the shuffle product, i.e. it exists an algebraic series b over K such that a̫b==1. Then a is a rational series. The same result is true when a and b are an algebraic series of many non-commutative variables. One application of this result is: If M is a linear system which is invertible, and with an output function ) and and N is a linear system with an output function ) suc such that N and the gen and the generating series H for M and G for N are both algebraic, then the systems M and N are bilinear.},
    date-added = {2024-1-13 16:53:14 +0100}
}

@article{LAMECHE19991, title = {Inverse for the shuffle for algebraic series}, journal = {Applied Mathematics and Computation}, volume = {98}, number = {1}, pages = {1-27}, year = {1999}, issn = {0096-3003}, doi = {https://doi.org/10.1016/S0096-3003(97)10059-5}, url = {https://www.sciencedirect.com/science/article/pii/S0096300397100595}, author = {Khira Lameche}, abstract = {Let K be a commutative field of characteristic 0, and a an algebraic series of one variable with coefficients in K, which is invertible for the shuffle product, i.e. it exists an algebraic series b over K such that a̫b==1. Then a is a rational series. The same result is true when a and b are an algebraic series of many non-commutative variables. One application of this result is: If M is a linear system which is invertible, and with an output function ) and and N is a linear system with an output function ) suc such that N and the gen and the generating series H for M and G for N are both algebraic, then the systems M and N are bilinear.}, date-added = {2024-1-13 16:53:14 +0100} }