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math.CO2026
Lozenge Tilings of Hexagons with Intrusions II: Shuffling Phenomenon
Seok Hyun Byun, Tri Lai
The enumeration of lozenge tilings of hexagons with holes has been studied intensively in recent years. Researchers tried to find shapes and positions of holes in hexagonal regions…
math.CO2026
Domino Tilings of Cruciform Regions
Tri Lai, Anh Thi Nguyen
P. Di Francesco first introduced the "Aztec triangle" in his study of the relationship between the twenty-vertex model and domino tilings. He conjectured an exact formula for the n…
math.CO2024
Lozenge Tilings of Hexagons with Intrusions I: Generalized Intrusion
Seok Hyun Byun, Tri Lai
MacMahon's classical theorem on the number of boxed plane partitions has been generalized in several directions. One way to generalize the theorem is to view boxed plane partitions…