Aperiodic Linearly Repetitive Delone Sets Are Densely Repetitive
نویسندگان
چکیده
منابع مشابه
Aperiodic Linearly Repetitive Delone Sets Are Densely Repetitive
We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.
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 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 کاملNon-repetitive colorings of infinite sets
In this paper we investigate colorings of sets avoiding similarly colored subsets. If S is an arbitrary colored set and T is a "xed family of bijections of S to itself, then two subsets A; B ⊆ S are said to be colored similarly with respect to T, if there exists a transformation t ∈T mapping A onto B, and preserving a coloring of A. This general setting covers some well-known topics such as non...
متن کاملSubstitution Delone Sets
Substitution Delone set families are families of Delone sets X = (X1, . . . ,Xn) which satisfy the inflation functional equation
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-003-2903-z