相关论文: Aztec Diamonds and Baxter Permutations
This paper is motivated by computing correlations for domino tilings of the Aztec diamond. It is inspired by two of the three distinct methods that have recently been used in the simplest case of a doubly periodic weighting, that is the…
The problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting (perfect) matchings of some subgraph of an Aztec diamond graph A_n, or more generally calculating the sum of the weights…
We introduce a new method for studying gap probabilities in a class of discrete determinantal point processes with double contour integral kernels. This class of point processes includes uniform measures of domino and lozenge tilings as…
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating matchings of planar graphs, up to matrix operations on their rows and columns. If such a matrix is defined over a principal ideal domain, this is equivalent to…
We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.
The author gave a proof of a generalization of the Aztec diamond theorem for a family of $4$-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in (Electron. J. Combin., 2014) by using a bijection between…
Discrete and continuous non-intersecting random processes have given rise to critical "infinite dimensional diffusions", like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large…
We study the asymptotic behavior of random domino tilings of the Aztec diamond of size $M$ in a random environment, where the environment is a one-periodic sequence of i.i.d. random weights attached to domino positions (i.e., to the edges…
In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable `temperate zone' in the interior…
We provide a new description of the scaling limit of dimer fluctuations in homogeneous Aztec diamonds via the intrinsic conformal structure of a space-like maximal surface in the three-dimensional Minkowski space $\mathbb{R}^{2,1}$. This…
We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it…
Inspired by Propp's intruded Aztec diamond regions, we consider halved hexagons in which two aligned arrays of triangular holes have been removed from their boundaries. Unlike the intruded Aztec diamonds (whose numbers of domino tilings…
Motivated in part by Propp's intruded Aztec diamond regions, we consider hexagonal regions out of which two horizontal chains of triangular holes (called ferns) are removed, so that the chains are at the same height, and are attached to the…
We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the…
We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given…
We consider uniform random domino tilings of the restricted Aztec diamond which is obtained by cutting off an upper triangular part of the Aztec diamond by a horizontal line. The restriction line asymptotically touches the arctic circle…
Baxter permutations are a class of permutations which are in bijection with a class of floorplans that arise in chip design called mosaic floorplans. We study a subclass of mosaic floorplans called $HFO_k$ defined from mosaic floorplans by…
We build a new perspective to count perfect matchings of a given graph. This idea is motivated by a construction on the relative cohomology group of surfaces. As an application of our theory, we reprove the celebrated Aztec Diamond theorem,…
Di Francesco introduced Aztec triangles as combinatorial objects for which their domino tilings are equinumerous with certain sets of configurations of the twenty-vertex model that are the main focus of his article. We generalize Di…
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard…