Permute, Graph, Map, Derange
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2021
- DOI:
- 10.48550/arXiv.2111.05720
- arXiv:
- arXiv:2111.05720
- Bibcode:
- 2021arXiv211105720F
- Keywords:
-
- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- Mathematics - Number Theory;
- 05A16 (Primary) 05A05;
- 05A15;
- 11B37;
- 11B75;
- 05C80;
- 68Q87;
- 11Y60 (Secondary
- E-Print:
- 17 pages