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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
Tiling by rectangles and alternating current
, 2010
"... This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses directcurrent circuits. The new approach of the paper is an application of alternatingcurrent circuits. The following results ar ..."
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This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses directcurrent circuits. The new approach of the paper is an application of alternatingcurrent circuits. The following results
TILING SIMPLY CONNECTED REGIONS WITH RECTANGLES
"... Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NPcomplete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solve ..."
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Cited by 8 (6 self)
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Abstract. In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two rectangles is NPcomplete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can
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.
Tiling rectangles with holey polyominoes
, 2014
"... We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 7 polyominoes with 5 or fewer visible squares. 1 ..."
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We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 7 polyominoes with 5 or fewer visible squares. 1
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
Results 1  10
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