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The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis
"... Abstract. We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M. 1. ..."
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Abstract. We compute the number of rhombus tilings of a hexagon with sides N, M, N, N, M, N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M. 1.
Enumeration of Rhombus Tilings of a Hexagon Which Contain a Fixed Rhombus on Its Symmetry Axis (Extended Abstract)
 in: Proceedings of the Tenth Conference on Formal Power Series and Algebraic Combinatorics
"... We compute the number of rhombus tilings of a hexagon with sides N;M;N; N;M;N , which contain a fixed rhombus on the symmetry axis. A special case solves a problem posed by Jim Propp. ..."
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We compute the number of rhombus tilings of a hexagon with sides N;M;N; N;M;N , which contain a fixed rhombus on the symmetry axis. A special case solves a problem posed by Jim Propp.
Rhombus tilings: decomposition and space structure
, 2004
"... We study the spaces of rhombus tilings, i.e. the graphs whose vertices are tilings of a fixed zonotope, and two tilings are linked if one can pass from one to the other one by a local transformation, called flip. We first use a decomposition method to encode rhombus tilings and give a useful charact ..."
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Cited by 4 (2 self)
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We study the spaces of rhombus tilings, i.e. the graphs whose vertices are tilings of a fixed zonotope, and two tilings are linked if one can pass from one to the other one by a local transformation, called flip. We first use a decomposition method to encode rhombus tilings and give a useful
A (conjectural) 1/3Phenomenon For The Number Of Rhombus Tilings Of A Hexagon Which Contain A Fixed Rhombus
"... We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths 2n+a; 2n+b; 2n+c; 2n+a; 2n+b; 2n+c contains the (horizontal) rhombus with coordinates (2n + x; 2n + y) is equal to 1 3 + g a;b;c;x;y ..."
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We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths 2n+a; 2n+b; 2n+c; 2n+a; 2n+b; 2n+c contains the (horizontal) rhombus with coordinates (2n + x; 2n + y) is equal to 1 3 + g a;b;c
Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus in the centre
"... Abstract. We compute the number of rhombus tilings of a hexagon with side lengths a,b,c,a,b,c which contain the central rhombus and the number of rhombus tilings of a hexagon with side lengths a,b,c,a,b,c which contain the ‘almost central ’ rhombus above the centre. ..."
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Cited by 11 (0 self)
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Abstract. We compute the number of rhombus tilings of a hexagon with side lengths a,b,c,a,b,c which contain the central rhombus and the number of rhombus tilings of a hexagon with side lengths a,b,c,a,b,c which contain the ‘almost central ’ rhombus above the centre.
Rhombus tilings of a hexagon with two triangles missing on the symmetry axis
, 1998
"... We compute the number of rhombus tilings of a hexagon with sides n, n, N, n, n, N, where two triangles on the symmetry axis touching in one vertex are removed. The case of the common vertex being the center of the hexagon solves a problem posed by Propp. ..."
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Cited by 7 (0 self)
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We compute the number of rhombus tilings of a hexagon with sides n, n, N, n, n, N, where two triangles on the symmetry axis touching in one vertex are removed. The case of the common vertex being the center of the hexagon solves a problem posed by Propp.
Distances on Rhombus Tilings
"... The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flipconnected space (a flip is the elementary operation on rhombus tilings which rotates 180 ◦ a hexagon made of three rhombi). Motivated by the study of a quasicrystal growth model, we are here interested i ..."
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The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flipconnected space (a flip is the elementary operation on rhombus tilings which rotates 180 ◦ a hexagon made of three rhombi). Motivated by the study of a quasicrystal growth model, we are here interested
Hard Squares with Negative Activity and Rhombus Tilings of the Plane
"... Let Sm,n be the graph on the vertex set Zm×Zn in which there is an edge between (a, b) and(c, d) if and only if either (a, b) =(c, d ± 1) or (a, b) =(c ± 1,d) modulo (m, n). We present a formula for the Euler characteristic of the simplicial complex Σm,n of independent sets in Sm,n. In particular, w ..."
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Let Sm,n be the graph on the vertex set Zm×Zn in which there is an edge between (a, b) and(c, d) if and only if either (a, b) =(c, d ± 1) or (a, b) =(c ± 1,d) modulo (m, n). We present a formula for the Euler characteristic of the simplicial complex Σm,n of independent sets in Sm,n. In particular
Results 1  10
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171,755