TY - JOUR AU - Matsen, Frederick A. AU - Evans, Steven N. PY - 2012 DA - 2012/05/21 TI - Ubiquity of synonymity: almost all large binary trees are not uniquely identified by their spectra or their immanantal polynomials JO - Algorithms for Molecular Biology SP - 14 VL - 7 IS - 1 AB - There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such representations involve a specific labeling of the vertices or at least the leaves, and so it is natural to attempt to identify trees by some feature of the associated matrices that is invariant under relabeling. An obvious candidate is the spectrum of eigenvalues (or, equivalently, the characteristic polynomial). SN - 1748-7188 UR - https://doi.org/10.1186/1748-7188-7-14 DO - 10.1186/1748-7188-7-14 ID - Matsen2012 ER -