Fulman, Jason Mixing time for a random walk on rooted trees. (English) Zbl 1206.05092 Electron. J. Comb. 16, No. 1, Research Paper R139, 13 p. (2009). Summary: We define an analog of Plancherel measure for the set of rooted unlabeled trees on \(n\) vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order \(n^2\) steps are necessary and suffice for convergence to the stationary distribution. Cited in 3 Documents MSC: 05C81 Random walks on graphs 05C05 Trees 60C05 Combinatorial probability PDFBibTeX XMLCite \textit{J. Fulman}, Electron. J. Comb. 16, No. 1, Research Paper R139, 13 p. (2009; Zbl 1206.05092) Full Text: arXiv EuDML EMIS Online Encyclopedia of Integer Sequences: Product, over all vertices v of the rooted tree with Matula-Goebel number n, of the number of vertices in the subtree with root v. Number of ways to take apart the rooted tree corresponding to the Matula-Goebel number n by sequentially removing terminal edges. The Connes-Moscovici weight of the rooted tree with Matula-Goebel number n. It is defined as the number of ways to build up the rooted tree from the one-vertex tree by adding successively edges to the existing vertices. Sum(M(t)), where summation is over all rooted trees t with n vertices and M(t) is the number of ways to take apart t by sequentially removing terminal edges (see A206494).