2 citations · 2 across the 9 of their papers we have counts for
7 papers · 1 filter
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…
Apollonian Circle Packings: Number Theory
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a pack…
Bounds for Local Density of Sphere Packings and the Kepler Conjecture
Jeffrey C. Lagarias
This paper describes the local density inequality approach to getting upper bounds for sphere packing densities in R^n. This approach was first suggested by L. Fejes-Toth in 1956 t…
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups
Jeffrey C. Lagarias, Sandor Szabo
A spectral set in R^n is a set X of finite Lebesgue measure such that L^2(X) has an orthogonal basis of exponentials. It is conjectured that every spectral set tiles R^n by transla…