Symmetries of shamrocks. II: Axial shamrocks

Mihai Ciucu¹

¹Indiana University

The electronic journal of combinatorics, Tome 25 (2018) no. 2

Résumé

The first paper in this series 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.

Détail

DOI : 10.37236/7412

Classification : 05A15, 05A17
Mots-clés : lozenge tilings, plane partitions, MacMahon's boxed plane partitions theorem, product formulas