2020/10/13 by Finch, Steven
#05A15 #11B37 #11B75 #68Q87 #68R15 (Primary) 05A05 #97K50 #97N60 (Secondary) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)
paper · doi:10.48550/arxiv.2010.06643
Fix a positive integer N. Select an additive composition ξ of N uniformly out of 2N-1 possibilities. The interplay between the number of parts in ξ and the maximum part in ξ is our focus. It is not surprising that correlations ρ(N) between these quantities are negative; we earlier gave inconclusive evidence that limN → ∞ ρ(N) is strictly less than zero. A proof of this result would imply asymptotic dependence. We now retract our presumption in such an unforeseen outcome. Similar experimental findings apply when ξ is a 1-free composition, i.e., possessing only parts ≥ 2.