6 papers · 1 filter
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…
A reflection principle for nonintersecting paths and lozenge tilings with free boundaries
Seok Hyun Byun
Okada and Stembridge's Pfaffian formula for the enumeration of families of nonintersecting paths with fixed starting points and unfixed ending points has been widely used to resolv…
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…
A Note on One-Hole Domino Tilings of Squares and Rectangles
Seok Hyun Byun, Wayne Goddard
We consider the number of domino tilings of an odd-by-odd rectangle that leave one hole. This problem is equivalent to the number of near-perfect matchings of the odd-by-odd rectan…
Block diagonally symmetric lozenge tilings
Seok Hyun Byun, Yi-Lin Lee
We introduce a new symmetry class of both plane partitions and lozenge tilings of a hexagon, called the \textit{-block diagonal symmetry class}, where is a…
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…