In this paper we address the following question: When do two rooted trees have the same plucking polynomial? The solution provided in the present paper has an algebraic version (Theorem 2.5) and a geometric version (Theorem 1.2). Furthermore, we give a criterion for a sequence of non-negative integers to be realized as a rooted tree.
"Rooted trees with the same plucking polynomial." Osaka J. Math. 56 (3) 661 - 674, July 2019.