Permute, Graph, Map, Derange
Combinatorics
2022-01-25 v2 Discrete Mathematics
Number Theory
Abstract
We study decomposable combinatorial labeled structures in the exp-log class, specifically, two examples of type a=1 and two examples of type a=1/2. Our approach is to establish how well existing theory matches experimental data. For instance, the median length of the longest cycle in a random n-permutation is (0.6065...)*n, whereas the median length of the largest component in a random n-mapping is (0.7864...)*n. Unsolved problems are highlighted, in the hope that someone else might address these someday.
Cite
@article{arxiv.2111.05720,
title = {Permute, Graph, Map, Derange},
author = {Steven Finch},
journal= {arXiv preprint arXiv:2111.05720},
year = {2022}
}
Comments
17 pages; some problems now solved and clarifications newly provided