38 citations · 129 across the 36 of their papers we have counts for
43 papers
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…
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…
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…
Perfect matchings and spanning trees: squarishness, bijections and independence
Seok Hyun Byun, Mihai Ciucu
A number which is either the square of an integer or two times the square of an integer is called squarish. There are two main results in the literature on graphs whose number of p…
Boundary dents, the arctic circle and the arctic ellipse
Mihai Ciucu, Christian Krattenthaler
The original motivation for this paper goes back to the mid-1990's, when James Propp was interested in natural situations when the number of domino tilings of a region increases if…
Cruciform regions and a conjecture of Di Francesco
Mihai Ciucu
A recent conjecture of Di Francesco states that the number of domino tilings of a certain family of regions on the square lattice is given by a product formula reminiscent of the o…