Structure of spaces of rhombus tilings in the lexicograhic caseReportar como inadecuado

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1 LIP - Laboratoire de l-Informatique du Parallélisme 2 IUT - Institut Universitaire de Technologie de Roanne

Abstract : Rhombus tilings are tilings of zonotopes with rhombohedra. We study a class of \emphlexicographic rhombus tilings of zonotopes, which are deduced from higher Bruhat orders relaxing the unitarity condition. Precisely, we fix a sequence $v 1, v 2,\dots, v D$ of vectors of $ℝ^d$ and a sequence $m 1, m 2,\dots, m D$ of positive integers. We assume lexicographic hypothesis that for each subsequence $v {i1}, v {i2},\dots, v {id}$ of length $d$, we have $detv {i1}, v {i2},\dots, v {id} > 0$. The zonotope $Z$ is the set $\{ Σα iv i 0 ≤α i ≤m i \}$. Each prototile used in a tiling of $Z$ is a rhombohedron constructed from a subsequence of d vectors. We prove that the space of tilings of $Z$ is a graded poset, with minimal and maximal element.

Keywords : rhombus tiling flip connectivity

Autor: Éric Rémila -



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