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SOLVABLE RECTANGLE TRIANGLE RANDOM TILINGS
, 1997
"... We show that a rectangle triangle random tiling with a tenfold symmetric phase is solvable by Bethe Ansatz. After the twelvefold square triangle and the eightfold rectangle triangle random tiling, this is the third example of a rectangle triangle tiling which is solvable. A Bethe Ansatz solution pro ..."
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We show that a rectangle triangle random tiling with a tenfold symmetric phase is solvable by Bethe Ansatz. After the twelvefold square triangle and the eightfold rectangle triangle random tiling, this is the third example of a rectangle triangle tiling which is solvable. A Bethe Ansatz solution
The Exact Solution of an Octagonal Rectangle Triangle Random Tiling
, 1996
"... We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eightfold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the sa ..."
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the same features as the squaretriangle random tiling model. We use the method of P. Kalugin, who solved the Bethe Ansatz equations for the squaretriangle tiling, which were found by M. Widom. Random tiling models are ensembles of coverings of the plane, without gaps or overlaps, with a set of rigid
Tilings of orthogonal polygons with similar rectangles or triangles
 Journal of Applied Mathematics & Computing
"... Abstract. In this paper we prove two results about tilings of orthogonal polygons. (1) Let P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u is algebra ..."
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Cited by 2 (0 self)
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braic and the real part of each of its conjugates is positive; (2) Laczkovich proved that if a triangle ∆ tiles a rectangle then either ∆ is a right triangle or the angles of ∆ are rational multiples of pi. We generalize the result of Laczkovich to orthogonal polygons. AMS Mathematical Subject Classification: 52C20.
Tiles and colors
, 2008
"... Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of twodimensional tiling models in which the tiles are rectangles and isosceles triangles. Some of these models ..."
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Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of twodimensional tiling models in which the tiles are rectangles and isosceles triangles. Some of these models
TILINGS OF PARALLELOGRAMS WITH SIMILAR TRIANGLES
"... Abstract. We say that a triangle ∆ tiles the polygon P if P can be decomposed into finitely many nonoverlapping triangles similar to ∆. Let P be a parallelogram with angles δ and pi − δ (0 < δ ≤ pi/2) and let ∆ be a triangle with angles α, β, γ (α ≤ β ≤ γ). We prove that if ∆ tiles P then either ..."
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triangle, linear space, tiling. We say that a triangle ∆ tiles the polygon P if P can be decomposed into finitely many nonoverlapping triangles similar to ∆. In [8] Szegedy considered the tilings of the square with similar right triangles and in [5] Laczkovich discussed the tilings of rectangles
RANDOM INFINITE SQUARINGS OF RECTANGLES
"... Abstract. A recent preprint [1] introduced a growth procedure for planar maps, whose almost sure limit is “the uniform infinite 3connected planar map”. A classical construction of Brooks, Smith, Stone and Tutte [7] associates a squaring of a rectangle (i.e. a tiling of a rectangle by squares) to a ..."
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Abstract. A recent preprint [1] introduced a growth procedure for planar maps, whose almost sure limit is “the uniform infinite 3connected planar map”. A classical construction of Brooks, Smith, Stone and Tutte [7] associates a squaring of a rectangle (i.e. a tiling of a rectangle by squares
Random Tilings: Concepts and Examples
 J. PHYS. A: MATH. GEN
, 1998
"... We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we pr ..."
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Cited by 16 (10 self)
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prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the reinterpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second
Random Dyadic Tilings of the Unit Square
, 2001
"... A "dyadic rectangle" is a set of the form R = [a2 s , (a+1)2 s ][b2 t , (b+1)2 t ], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study ntilings which consist of 2 n nonoverlapping dyadic rectangles, ..."
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Cited by 2 (0 self)
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A "dyadic rectangle" is a set of the form R = [a2 s , (a+1)2 s ][b2 t , (b+1)2 t ], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study ntilings which consist of 2 n nonoverlapping dyadic rectangles
Results 1  10
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