منابع مشابه
Distances on Lozenge Tilings
In this paper, a structural property of the set of lozenge tilings of a 2n-gon is highlighted. We introduce a simple combinatorial value called Hamming-distance, which is a lower bound for the flipdistance (i.e. the number of necessary local transformations involving three lozenges) between two given tilings. It is here proven that, for n ≤ 4, the flip-distance between two tilings is equal to t...
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It is well-known that plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection. In this work we consider regions that are more general than hexagons. They are obtained by further removing upward-pointing triangles. We call the resulting shapes triangular regions. We establish signed v...
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We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the HarishChandra/Itzykson-Zuber integra...
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We consider tilings of quadriculated regions by dominoes and of triangulated regions by lozenges. We present an overview of results concerning tileability, enumeration and the structure of the space of tilings.
متن کاملEnumeration of Lozenge Tilings of Punctured Hexagons
We present a combinatorial solution to the problem of determining the number of lozenge tilings of a hexagon with sides a, b + 1, b, a + 1, b, b + 1, with the central unit triangle removed. For a = b, this settles an open problem posed by Propp 7]. Let a, b, c be positive integers, and denote by H the hexagon whose side-lengths are (in cyclic order) a, b, c, a, b, c and all whose angles have 12...
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2015
ISSN: 0377-9017,1573-0530
DOI: 10.1007/s11005-015-0794-6