Maximum Wealth Trees

Associate a positive number, called an asset, to each nonterminal node of a t-ary tree, i.e., a rooted directed tree with outdegree t at each nonterminal node. The heritage of a node is the product of the assets of all its ancestors. The wealth of a tree is the sum of the heritages of its terminal nodes. For a given set of m assets, we give a simple construction for finding a t-ary tree with m nonterminal nodes and an assignment of the m assets to the m nonterminal nodes to achieve maximum wealth. Maximum wealth trees have applications in designing experiments to select a most probable event and in designing tournaments to identify a best player.