Rhombus tilings: decomposition and space structure
نویسندگان
چکیده
منابع مشابه
Rhombus Tilings: Decomposition and Space Structure
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 characterization for a sequence of bits to encode a tiling. In codimension 2, we use the previous coding...
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The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected 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 in better understanding how “tight” rhombus tiling spaces are flip-connected. We introduce a lower ...
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The algebraic relations between the principal minors of an n× n matrix are somewhat mysterious, see e.g. [LS09]. We show, however, that by adding in certain almost principal minors, the relations are generated by a single relation, the so-called hexahedron relation, which is a composition of six cluster mutations. We give in particular a Laurent-polynomial parameterization of the space of n× n ...
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Rhombus tilings are tilings of zonotopes with rhombohedra. We study a class of lexicographic rhombus tilings of zonotopes, which are deduced from higher Bruhat orders relaxing the unitarity condition. Precisely, we fix a sequence (v1, v2, . . . , vD) of vectors of R and a sequence (m1,m2, . . . ,mD) of positive integers. We assume (lexicographic hypothesis) that for each subsequence (vi1 , vi2 ...
متن کاملMixing Times of Plane Random Rhombus Tilings
We address the question of single flip discrete dynamics in sets of two-dimensional random rhombus tilings with fixed polygonal boundaries. Single flips are local rearrangements of tiles which enable to sample the configuration sets of tilings via Markov chains. We determine the convergence rates of these dynamical processes towards the statistical equilibrium distributions and we demonstrate t...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2004
ISSN: 1571-0653
DOI: 10.1016/j.endm.2004.06.013