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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 1, 2019, pp. 123–154
DOI: 10.4171/AIHPD/67

Published online: 2019-02-08

On a square-ice analogue of plane partitions

Suresh Govindarajan[1], Anthony J. Guttmann[2] and Varsha Subramanyan[3]

(1) Indian Insitute of Technolgy Madras, Chennai, India
(2) The University of Melbourne, Australia
(3) University of Illinois at Urbana-Champaign, USA

We study a one-parameter family $(\ell=1,2,3,…)$ 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.

Keywords: Plane partitions, square-ice, exact and asymptotic enumeration

Govindarajan Suresh, Guttmann Anthony, Subramanyan Varsha: On a square-ice analogue of plane partitions. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 123-154. doi: 10.4171/AIHPD/67