9 citations · 82 across the 42 of their papers we have counts for
7 papers · 1 filter
Double Aztec Rectangles
Tri Lai
We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a sim…
A new proof for the number of lozenge tilings of quartered hexagons
Tri Lai
It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the t…
A note on a 2-enumeration of antisymmetric monotone triangles
Tri Lai
In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author pr…
Enumeration of tilings of quartered Aztec rectangles
Tri Lai
We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to tran…
Proof of a refinement of Blum's conjecture on hexagonal dungeons
Tri Lai
Matt Blum conjectured that the number of tilings of a hexagonal dungeon with side-lengths (for ) equals . Ciucu and the…
Proof of Blum's conjecture on hexagonal dungeons
Mihai Ciucu, Tri Lai
Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of sides (where ) is (J. P…