2 citations · 2 across the 9 of their papers we have counts for
7 papers · 1 filter
Substitution Delone Sets
Jeffrey C. Lagarias, Yang Wang
This paper addresses the problem of describing aperiodic discrete structures that have a self-similar or self-affine structure. Substitution Delone set families are families of Del…
Local Complexity of Delone Sets and Crystallinity
J. C. Lagarias, P. A. B. Pleasants
This paper characterizes when a Delone set X 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 distr…
Beyond the Descartes circle theorem
Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks
The Descartes circle theorem states that if four circles are mutually tangent with disjoint intersion, then their curvatures (or "bends) b_j = 1/r_j satisfy the relation (b_1 + b_2…
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
This paper gives -dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all -dimensional oriented Descartes configu…
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms o…
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian pa…