2 citations · 2 across the 9 of their papers we have counts for
5 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…
Lower bounds for the total stopping time of 3X+1 iterates
David Applegate, Jeffrey C. Lagarias
The 3X+1 function T(n) is (3n+1)/2 if n is odd and n/2 if n is even. The total stopping time σ_\infty (n) for a positive integer n is the number of iterations of the 3x+1 function…
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…
On the Normality of Arithmetical Constants
Jeffrey C. Lagarias
D. Bailey and R. E. Crandall recently formulated a "Hypothesis A", which provides a general principle to explain the (conjectured) normality of constants like pi or log 2 and other…