article · Bristol Research (University of Bristol)
Untitled
Michael Albert, Cecilia Holmgren, Tony Johansson, Fiona Skerman
Cited by 3Open access
Abstract
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees. We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye in 1998. Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with high probability the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.
Cite this paper
Albert, M., Holmgren, C., Johansson, T., & Skerman, F. (n.d.). Untitled. Bristol Research (University of Bristol).
Albert, Michael, et al. “Untitled.” Bristol Research (University of Bristol).
Albert, Michael, Cecilia Holmgren, Tony Johansson, and Fiona Skerman. n.d.. “Untitled.” Bristol Research (University of Bristol).
Albert, M. et al. (n.d.) ‘Untitled’, Bristol Research (University of Bristol).
@article{albertuntitled,
title = {{Untitled}},
author = {Albert, Michael and Holmgren, Cecilia and Johansson, Tony and Skerman, Fiona},
journal = {Bristol Research (University of Bristol)}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.