167 citations · 519 across the 84 of their papers we have counts for
7 papers · 1 filter
The Kruskal Count
Jeffrey C. Lagarias, Eric Rains, Robert J. Vanderbei
The Kruskal Count is a card trick invented by Martin J. Kruskal in which a magician "guesses" a card selected by a subject according to a certain counting procedure. With high prob…
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…
On a two-variable zeta function for number fields
Jeffrey C. Lagarias, Eric Rains
This paper studies a zeta function of two complex variables (w, s) attached to an algebraic number field K, introduced by van der Geer and Schoof, which is based on an analogue of…
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…