On the automorphisms of rooted trees with height distributions

Abstract

Let UB(v) be the supremum of the orders of automorphism groups of rooted trees with height distribution v=(v₀,...,v_h). It is shown that among the set of rooted trees with height distribution v and automorphism group of order UB(v) there is always one with a very simple structure. The problem of finding an efficient algorithm to determine UB(v) in terms of the parameters v₀,...,v_h is considered and partial results obtained for some classes of height distributions v.