9 citations · 16 across the 7 of their papers we have counts for
7 papers
On Curling Numbers of Integer Sequences
Benjamin Chaffin, John P. Linderman, N. J. A. Sloane +1
Given a finite nonempty sequence S of integers, write it as XY^k, where Y^k is a power of greatest exponent that is a suffix of S: this k is the curling number of S. The Curling Nu…
A Slow-Growing Sequence Defined by an Unusual Recurrence
Fokko J. van de Bult, Dion C. Gijswijt, John P. Linderman +2
The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY^k, where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the…
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…