9 citations · 82 across the 42 of their papers we have counts for
6 papers · 1 filter
Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-octagonal regions
Tri Lai
We use the subgraph replacement method to prove a simple product formula for the tilings of an 8-vertex counterpart of Propp's quasi-hexagons (Problem 16 in New Perspectives in Geo…
A generalization of Aztec diamond theorem, part I
Tri Lai
We generalize Aztec diamond theorem (N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings, Journal Algebraic Combinatoric, 1992) by showin…
A simple proof for the number of tilings of quartered Aztec diamonds
Tri Lai
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the num…
Proof of a conjecture of Bauer, Fan and Veldman
Tri Lai
For a 1-tough graph we define is an independent set of vertices and . D. Bauer,…
Enumeration of Hybrid Domino-Lozenge Tilings
Tri Lai
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…
New aspects of regions whose tilings are enumerated by perfect powers
Tri Lai
In 2003, Ciucu presented a unified way to enumerate tilings of lattice regions by using a certain Reduction Theorem (Ciucu, Perfect Matchings and Perfect Powers, Journal of Algebra…