On a square-ice analogue of plane partitions

Suresh Govindarajan; Anthony J. Guttmann; Varsha Subramanyan

doi:10.4171/aihpd/67

JournalsaihpdVol. 6, No. 1pp. 123–154

On a square-ice analogue of plane partitions

Suresh Govindarajan
Indian Insitute of Technolgy Madras, Chennai, India
Anthony J. Guttmann
The University of Melbourne, Australia
Varsha Subramanyan
University of Illinois at Urbana-Champaign, USA

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Abstract

We study a one-parameter family $(ℓ = 1, 2, 3, \dots)$ 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. 123–154

DOI 10.4171/AIHPD/67