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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.
@article{AIHPD_2019__6_1_123_0, author = {Govindarajan, Suresh and Guttmann, Anthony J. and Subramanyan, Varsha}, title = {On a square-ice analogue of plane partitions}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {123--154}, volume = {6}, number = {1}, year = {2019}, doi = {10.4171/aihpd/67}, mrnumber = {4033534}, zbl = {1407.05013}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/67/} }
TY - JOUR AU - Govindarajan, Suresh AU - Guttmann, Anthony J. AU - Subramanyan, Varsha TI - On a square-ice analogue of plane partitions JO - Annales de l’Institut Henri Poincaré D PY - 2019 SP - 123 EP - 154 VL - 6 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpd/67/ DO - 10.4171/aihpd/67 LA - en ID - AIHPD_2019__6_1_123_0 ER -
%0 Journal Article %A Govindarajan, Suresh %A Guttmann, Anthony J. %A Subramanyan, Varsha %T On a square-ice analogue of plane partitions %J Annales de l’Institut Henri Poincaré D %D 2019 %P 123-154 %V 6 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpd/67/ %R 10.4171/aihpd/67 %G en %F AIHPD_2019__6_1_123_0
Govindarajan, Suresh; Guttmann, Anthony J.; Subramanyan, Varsha. On a square-ice analogue of plane partitions. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 1, pp. 123-154. doi : 10.4171/aihpd/67. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/67/
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