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arXiv · 1906.02951

Centrally symmetric tilings of fern-cored hexagons

Mihai Ciucu
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Abstract

In this paper we enumerate the centrally symmetric lozenge tilings of a hexagon with a fern removed from its center. The proof is based on a variant of Kuo's graphical condensation method. An unexpected connection with the total number of tilings is established~---~when suitably normalized, the number of centrally symmetric tilings is equal to the square root of the total number of tilings. The results we present can be regarded as a new extension of the enumeration of self-complementary plane partitions that fit in a box.

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Mihai Ciucu. 2019-06-07. Centrally symmetric tilings of fern-cored hexagons. https://arxiv.org/abs/1906.02951

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