Maurice Ginocchio - On the bialgebra of functional graphs and differential algebras

dmtcs:244 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 - https://doi.org/10.46298/dmtcs.244
On the bialgebra of functional graphs and differential algebras

Authors: Maurice Ginocchio

    We develop the bialgebraic structure based on the set of functional graphs, which generalize the case of the forests of rooted trees. We use noncommutative polynomials as generating monomials of the functional graphs, and we introduce circular and arborescent brackets in accordance with the decomposition in connected components of the graph of a mapping of \1, 2, \ldots, n\ in itself as in the frame of the discrete dynamical systems. We give applications fordifferential algebras and algebras of differential operators.


    Volume: Vol. 1
    Published on: January 1, 1997
    Imported on: March 26, 2015
    Keywords: noncommutative polynomials,bialgebraic structure,functional graphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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