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

dmtcs:244 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 -
On the bialgebra of functional graphs and differential algebrasArticle

Authors: Maurice Ginocchio 1

  • 1 Laboratoire de Physique Théorique et Mathématique [Paris 7]

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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