A dual of MacMahon's theorem on plane partitions
Combinatorics
2021-06-01 v1
Abstract
A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this paper we present a counterpart of this formula, corresponding to the {\it exterior} of a concave hexagon obtained by turning 120 degrees after drawing each side (MacMahon's hexagon is obtained by turning 60 degrees after each step).
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Cite
@article{arxiv.1210.5506,
title = {A dual of MacMahon's theorem on plane partitions},
author = {Mihai Ciucu and Christian Krattenthaler},
journal= {arXiv preprint arXiv:1210.5506},
year = {2021}
}
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22 pages