Enumeration of tilings of diamonds and hexagons with defects

Abstract

We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to problems 1, 2, and 10 in James Propp's list of problems on enumeration of matchings.

References in corpus (3)

• Alternating sign matrices and domino tilings
• The shape of a typical boxed plane partition
• Twenty Open Problems in Enumeration of Matchings

Cited by in corpus (8)

• Modular Design of Hexagonal Phased Arrays Through Diamond Tiles
• A $q$-enumeration of lozenge tilings of a hexagon with three dents
• Plane partitions of shifted double staircase shape
• An extension of the Lindström-Gessel-Viennot theorem
• Enumeration of symmetric centered rhombus tilings of a hexagon
• Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-octagonal regions
• Enumeration of Hybrid Domino-Lozenge Tilings
• Enumeration of tilings of quartered Aztec rectangles