Symmetries of shamrocks. II: Axial shamrocks
type: Item
instance of: scholarly article
title: Symmetries of shamrocks. II: Axial shamrocks
zbMATH Open document ID: 1388.05012
author: Mihai Ciucu
published in: The Electronic Journal of Combinatorics
publication date: 2018-06-14T00:00:00Z
full work available at URL: v25i2p36
review text: 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.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 6888445
zbMATH Keywords: lozenge tilings
zbMATH Keywords: plane partitions
zbMATH Keywords: MacMahon's boxed plane partitions theorem
zbMATH Keywords: product formulas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6888445