A $q$-enumeration of lozenge tilings of a hexagon with three dents

Abstract

We $q$-enumerate lozenge tilings of a hexagon with three bowtie-shaped regions have been removed from three non-consecutive sides. The unweighted version of the result generalizes a problem posed by James Propp on enumeration of lozenge tilings of a hexagon of side-lengths $2n,2n+3,2n,2n+3,2n,2n+3$ (in cyclic order) with the central unit triangles on the $(2n+3)$-sides removed.

33 pages. The title has been changed

References in corpus (4)

• Condensation of Determinants
• Graphical Condensation Generalizations Involving Pfaffians and Determinants
• Cluster Variables and Perfect Matchings of Subgraphs of the $d{P}_3$ Lattice
• A Generalization of Aztec Dragons

Cited by in corpus (1)

• Enumeration of lozenge tilings of a hexagon with a maximal staircase and a unit triangle removed