3 papers
math.CO2025
Propp's benzels and Lai's nearly symmetric hexagons with holes
Seok Hyun Byun, Mihai Ciucu, Yi-Lin Lee
In this paper we present a new version of the second author's factorization theorem for perfect matchings of symmetric graphs. We then use our result to solve four open problems of…
math.CO2025
Round Aztec windows, a dual of the Aztec diamond theorem and a curious symmetry of the correlation of diagonal slits
Mihai Ciucu
Fairly shortly after the publication of the Aztec diamond theorem of Elkies, Kuperberg, Larsen and Propp in 1992, interest arose in finding the number of domino tilings of an Aztec…
math.CO2025
A short combinatorial proof of Di Francesco's conjecture on Aztec triangles
Seok Hyun Byun, Mihai Ciucu
Di Francesco conjectured in 2021 that the number of domino tilings of a certain family of regions -- called Aztec triangles -- on the square lattice is given by a product formula r…