منابع مشابه
Substitution Delone Sets
Substitution Delone set families are families of Delone sets X = (X1, . . . ,Xn) which satisfy the inflation functional equation
متن کاملRepetitive Delone Sets and Quasicrystals
This paper studies the problem of characterizing the simplest aperiodic discrete point sets, using invariants based on topological dynamics. A Delone set of finite type is a Delone set X such that X −X is locally finite. Such sets are characterized by their patch-counting function NX(T ) of radius T being finite for all T . We formulate conjectures relating slow growth of the patch-counting fun...
متن کاملLocal Complexity of Delone Sets and
This paper characterizes when a Delone setX in Rn is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. For a Delone set X, let NX(T ) count the number of translation-inequivalent patches of radius T in X and let MX(T ) be the minimum radius such that every closed ball of radius MX(T ) contains the center ...
متن کاملRepetitive Delone Sets and Perfect QuasicrystalsJe
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set of nite type is a Delone set X such that X ? X is locally nite. Such sets are characterized by their patch-counting function N X (T) of radius T being nite for all T. A Delone set X of nite type is repetitive if there is a function ...
متن کاملSidon sets and Riesz products
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1998
ISSN: 0386-2194
DOI: 10.3792/pjaa.74.1