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Fixedboundary octagonal random tilings: a combinatorial approach
 J. Stat. Phys
, 2001
"... Abstract. Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus generalizing previous results on the more restricte ..."
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Cited by 7 (5 self)
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Abstract. Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus generalizing previous results on the more restricted class of codimensionone tilings. In particular this method gives access to counting formulas, which are directly related to questions of entropy in these statistical systems. Methods and tools from the field of enumerative combinatorics are used. Keywords: Random tilings – Generalized partitions – Configurational entropy – Discrete dynamical systems – Young tableaux.
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 have been solved recently by means of Bethe Ansatz. We discuss the question why only these models in a larger family are solvable, and we search for the YangBaxter structure behind their integrablity. In this quest we find the Bethe Ansatz solution of the problem of coloring the edges of the square lattice in four colors, such that edges of the same color never meet in the same vertex.
Laboratory of Atomic and Solid State Physics, Cornell University,
, 1999
"... Dedicated to the memory of Marko V. Jarić ..."
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