Polyboxes, Cube Tilings and Rigidity

被引：0
作者：
Andrzej P. Kisielewicz
Krzysztof Przesławski
机构：
[1] Uniwersytet Zielonogórski,Wydział Matematyki, Informatyki i Ekonometrii
来源：
Discrete & Computational Geometry | 2008年 / 40卷
关键词：
Box; Dichotomous boxes; Polybox; Additive mapping; Index; Binary code; Word; Genome; Cube tiling; Rigidity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A non-empty subset A of X=X1×⋅⋅⋅×Xd is a (proper) box if A=A1×⋅⋅⋅×Ad and Ai⊂Xi for each i. Suppose that for each pair of boxes A, B and each i, one can only know which of the three states takes place: Ai=Bi, Ai=Xi∖Bi, Ai∉{Bi,Xi∖Bi}. Let F and G be two systems of disjoint boxes. Can one decide whether ∪F=∪G? In general, the answer is ‘no’, but as is shown in the paper, it is ‘yes’ if both systems consist of pairwise dichotomous boxes. (Boxes A, B are dichotomous if there is i such that Ai=Xi∖Bi.) Several criteria that enable to compare such systems are collected. The paper includes also rigidity results, which say what assumptions have to be imposed on F to ensure that ∪F=∪G implies F=G. As an application, the rigidity conjecture for 2-extremal cube tilings of Lagarias and Shor is verified.
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页码：1 / 30
页数：29
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