2021/11/10 by Finch, Steven
#05A15 #05A16 (Primary) 05A05 #05C80 #11B37 #11B75 #11Y60 (Secondary #68Q87 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2111.05720
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.