Symmetries of shamrocks. II: Axial shamrocks
Summary: The first paper in this series [the author, J. Comb. Theory, Ser. A 155, 376--397 (2018; Zbl 1377.05086)] presented the enumeration of cyclically symmetric, and cyclically symmetric and transpose complementary lozenge tilings of a hexagon with a shamrock removed from its center. In this article we address the transpose complementary case. The results we prove are in fact more general and allow us to give an extension of the symmetric case of the original hexagonal regions with shamrocks removed from their center, to what we call axial shamrocks. For the latter, the transpose complementary case is the only symmetry class besides the one requiring no symmetries. The enumeration of both of these follows from our results.
MacMahon's boxed plane partitions theorem
scientific article; zbMATH DE number 6888445
scientific article