Tri Lai

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

We

Enumeration of hybrid domino-lozenge tilings

q

Proof of Blum's conjecture on hexagonal dungeons

-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

A q-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundary

2n,2n+3,2n,2n+3,2n,2n+3

BEYOND AZTEC CASTLES:TORIC CASCADES IN THE dP 3 QUIVER

(in cyclic order) with the central unit triangles on the

A Generalization of Aztec Dragons

(2n+3)

A generalization of Aztec diamond theorem, part II

-sides removed.

Proof of a conjecture of Kenyon and Wilson on semicontiguous minors

We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas? theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

Lozenge Tilings of a Halved Hexagon with an Array of Triangles Removed from the Boundary

Abstract Matt Blum conjectured that the number of tilings of the hexagonal dungeon of sides a, 2a, b, a, 2a, b (where b ⩾ 2 a ) is 13 2 a 2 14 ⌊ a 2 2 ⌋ (Propp, 1999 [4] ). In this paper we present a proof for this conjecture using Kuos Graphical Condensation Theorem (Kuo, 2004 [2] ).

Generating Function of the Tilings of an Aztec Rectangle with Holes

Abstract MacMahon proved a simple product formula for the generating function of plane partitions fitting in a given box. The theorem implies a q -enumeration of lozenge tilings of a semi-regular hexagon on the triangular lattice. In this paper we generalize MacMahon’s classical theorem by q -enumerating lozenge tilings of a new family of hexagons with four adjacent triangles removed from their boundary.