We give a bijective proof of the Aztec diamond theorem, stating that there are 2n(n+1)/2 domino tilings of the Aztec diamond of order n. The proof in fact es-tablishes a similar result for non-intersecting families of n+ 1 Schröder paths, with horizontal, diagonal or vertical steps, linking the grid points of two adjacent sides of an n × n square grid; these families are well known to be in bijection with tilings of the Aztec diamond. Our bijection is produced by an invertible “combing ” algorithm, operating on families of paths without non-intersection condition, but instead with the requirement that any vertical steps come at the end of a path, and which are clearly 2n(n+1)/2 in number; it transforms them into non-intersecting families.
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can co...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
We introduce a family of planar regions, called Aztec diamonds, and study the ways in which...
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagona...
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagona...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can co...
Abstract. We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyr...
AbstractIn this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we ...
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing ...
AbstractIn this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we ...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can co...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
We introduce a family of planar regions, called Aztec diamonds, and study the ways in which...
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagona...
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagona...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Tilings over the plane are analysed in this work, making a special focus on the Aztec Diamond Theore...
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can co...
Abstract. We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyr...
AbstractIn this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we ...
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing ...
AbstractIn this paper, we continue the study of domino-tilings of Aztec diamonds. In particular, we ...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can co...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
We introduce a family of planar regions, called Aztec diamonds, and study the ways in which...