Dependence of tree copy functions (Q1058532)

The graph copy function when restricted to the set of trees or of rooted trees is called the tree copy function or the rooted tree copy function, respectively. We show that both the set of tree copy functions and the set of rooted tree copy functions are strongly linearly independent. We also show that the set of all tree copy functions are algebraically independent but the set of all rooted tree copy functions are not. An algebraic base for the algebra generated by rooted tree copy functions is constructed in this paper.