167 citations · 519 across the 84 of their papers we have counts for
11 papers · 1 filter
Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem
Rob Kusner, Wöden Kusner, Jeffrey C. Lagarias +1
The problem of twelve spheres is to understand, as a function of , the configuration space of non-overlapping equal spheres of radius touching a cen…
Moser's Shadow Problem
Jeffrey C. Lagarias, Yusheng Luo, Arnau Padrol
Moser's shadow problem asks to estimate the shadow function , which is the largest number such that for each bounded convex polyhedron with vertices in $…
p-adic path set fractals and arithmetic
William Abram, Jeffrey C. Lagarias
This paper considers a class C(Z_p) of closed sets of the p-adic integers obtained by graph-directed constructions analogous to those of Mauldin and Williams over the real numbers.…
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…