scholarly journals Domino tilings of rectangles with fixed width

1980 ◽  
Vol 32 (1) ◽  
pp. 45-52 ◽  
Author(s):  
David Klarner ◽  
Jordan Pollack
Keyword(s):  
Domino Tilings

scholarly journals A Gessel–Viennot-Type Method for Cycle Systems in a Directed Graph

10.37236/1063 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Christopher R. H. Hanusa
Keyword(s):  
Directed Graph ◽  
Type Method ◽  
Domino Tilings ◽  
Cycle Systems ◽  
Insight Into

We introduce a new determinantal method to count cycle systems in a directed graph that generalizes Gessel and Viennot's determinantal method on path systems. The method gives new insight into the enumeration of domino tilings of Aztec diamonds, Aztec pillows, and related regions.

scholarly journals Tiling Parity Results and the Holey Square Solution

10.37236/1874 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
Bridget Eileen Tenner
Keyword(s):  
Domino Tilings

We prove combinatorially that the parity of the number of domino tilings of a region is equal to the parity of the number of domino tilings of a particular subregion. Using this result we can resolve the holey square conjecture. We furthermore give combinatorial proofs of several other tiling parity results, including that the number of domino tilings of a particular family of rectangles is always odd.

scholarly journals Domino tilings and related models: space of configurations of domains with holes

2004 ◽  
Vol 319 (1-3) ◽  
pp. 83-101 ◽  
Author(s):  
Sébastien Desreux ◽  
Martin Matamala ◽  
Ivan Rapaport ◽  
Eric Rémila
Keyword(s):  
Domino Tilings

Domino Tilings and Determinants

2014 ◽  
Vol 200 (6) ◽  
pp. 647-653 ◽  
Author(s):  
V. Aksenov ◽  
K. Kokhas
Keyword(s):  
Domino Tilings

scholarly journals Aztec Diamonds and Baxter Permutations

10.37236/377 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Hal Canary
Keyword(s):  
Permutation Matrix ◽  
Enumerative Combinatorics ◽  
Alternating Sign Matrices ◽  
Domino Tilings ◽  
Permutation Matrices ◽  
Pattern Avoiding Permutations ◽  
The Relationship

We present a proof of a conjecture about the relationship between Baxter permutations and pairs of alternating sign matrices that are produced from domino tilings of Aztec diamonds. It is shown that a tiling corresponds to a pair of ASMs that are both permutation matrices if and only if the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literature on both pattern-avoiding permutations of various kinds [Baxter 1964, Dulucq and Guibert 1988] and tilings of regions using dominos or rhombuses as tiles [Elkies et al. 1992, Kuo 2004]. However, there have not as of yet been many links between these two areas of enumerative combinatorics. This paper gives one such link.

scholarly journals Symmetric matrices, Catalan paths, and correlations

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Emmanuel Tsukerman ◽  
Lauren Williams ◽  
Bernd Sturmfels
Keyword(s):  
Laurent Polynomial ◽  
Symmetric Matrices ◽  
Correlation Matrices ◽  
Domino Tilings ◽  
Aztec Diamond ◽  
International Audience ◽  
Square Matrix

International audience Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametrization for symmetric matrices, where the Laurent monomials are indexed by Catalan paths. In this paper we prove the Kenyon-Pemantle conjecture, and apply this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope.

Problem 250. Correlations in random domino tilings.

1996 ◽  
Vol 157 (1-3) ◽  
pp. 377-378
Author(s):  
J Propp
Keyword(s):  
Domino Tilings
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