2020/03/25 by Mutafchiev, Ljuben
#05A16 #05A17 #11P82 #60F05 #Combinatorics (math.CO) #FOS: Mathematics #G.2 #G.3
paper · doi:10.48550/arxiv.2003.11577
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the positive integer n, introduced by Stanley in 1973. We derive generating functions and determine the asymptotic behavior of counts of large parts using a general scheme based on the saddle point method. In this way, we are able to prove a Poisson limit theorem for the number of parts of a random and uniformly chosen plane partition of n, whose sizes are greater than a function m=m(n) as n→∞. An explicit expression for m(n) is also given.