We study a one-parameter family of configurations that are square-ice analogues of plane partitions. Using an algorithm due to Bratley and McKay, we carry out exact enumerations in order to study their asymptotic behaviour and establish, via Monte Carlo simulations as well as explicit bounds, that the asymptotic behaviour is similar to that of plane partitions. We finally carry out a series analysis and provide independent estimates for the asymptotic behaviour.
Cite this article
Suresh Govindarajan, Anthony J. Guttmann, Varsha Subramanyan, On a square-ice analogue of plane partitions. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), no. 1, pp. 123–154DOI 10.4171/AIHPD/67