Discrete Mathematics & Theoretical Computer Science, Vol 1 (1997)

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DMTCS vol 1 no 1 (1997), pp. 229-237

Discrete Mathematics & Theoretical Computer Science


Volume 1 n° 1 (1997), pp. 229-237

author:Maurice Ginocchio
title:On the bialgebra of functional graphs and differential algebras
keywords:bialgebraic structure, functional graphs, noncommutative polynomials
abstract: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, ...n} in itself as in the frame of the discrete dynamical systems. We give applications fordifferential algebras and algebras of differential operators.
reference: Maurice Ginocchio (1997), On the bialgebra of functional graphs and differential algebras, Discrete Mathematics and Theoretical Computer Science 1, pp. 229-237
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