Publications

 

History

Mathematics in Uganda

Fractal Geometry

Thresholds for One-Parameter Families of Affine Iterated Function Systems
Global Fractal Transformations and Global Addressing
Approximation of Rough Functions
Old wine in fractal bottles I: orthogonal expansions on self-referential spaces via fractal transformations
Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
Developments in Fractal Geometry
Fractal Continuation
The Conley Attractors of an Iterated Function System
Embedding the Symbolic Dynamics of Lorenz Maps
The Entropy of a Special Overlapping Dynamical System
Mobius Iterated Function Systems
Fractal Homeomorphism for Bi-affine Iterated Function System
The Eigenvalue Problem for Linear and Affine Iterated Function Systems
Real Projective Iterated Function Systems
The Chaos Game on a General Iterated Function System
A Characterization of Hyperbolic Affine Iterated Function Systems

Algebraic and Geometric Combinatorics

A combinatorial approach to binary positional number systems
Critical itineraries of maps with constant slope and one discontinuity
Enumeration of Viral Capsid Pathways: tree orbits under permutation group action
Orthogonal Matroids
An Adjacency Criterion for Coxeter Matroids
The Lattice of Flats and its Underlying Flag Polytope
A Geometric Characterization of Coxeter Matroids
Variations on a Theorem of Ryser
Non-Revisiting Paths on Surfaces with Low Genus
Non-Revisiting Paths on Surfaces
Map Duality and Generalizations
The Classification of Closed Surfaces Using Colored Graphs
A Shellable Poset that is not Lexicographically Shellable
Graphic Matroids, Shellability and the Poincaré Conjecture
Regular Combinatorial Maps
Combinatorial Maps
Period of a Linear Recurrence

Tiling

Tilings from Graph Directed Iterated Functiion Systems
Self-Similar Polygonal Tiling
Fractal Tiling for an Iterated Function System
A Property of Normal Tilings
Digit Tiling of Euclidean Space
The Hausdorff Dimension of the Boundary of a Self-Similar Tile
Self-Replicating Tiles and their Boundary
Periodicity, Quasiperiodicity, and Bieberbach’s Theorem on Crystallographic Groups
Isohedral Polyomino Tiling of the Plane
Replicating Tessellations
Rep-Tiling Euclidean Space
An Isomorphism between the p-adic Integers and a Ring Associated with a Tiling

Graph Theory

The Average Size of a Connected Vertex Set of a Graph
Contractive Digraphs and Splicing Machines
The Maximum Matroid for a Graph
Counting Connected Sets and Connected Partitions of a Graph
The Number of Ways to Assemble a Graph
The Average Order of a Subtree of a Tree
Infinitely Many Trees have the Non-Sperner Subtree Property
Parity Versions of 2-Connectedness
The Integrity of a Cubic Graph
Maps (in Handbook of Graph Theory)
Graph Recurrence
Geodesics in Graphs,
An Extremal Set Problem, and Perfect Hash Families

The Separation Index of a Graph
On Representations of Some Thickness-Two Graphs
Cycles in a Graph of Lengths Differ by One or Two
Reconstruction of the Set of Branches of a Graph
The Spectral Radius of a Planar Graph
Dyck’s Map (3,7)_8 is a Counterexample to a Clique Covering Conjecture
Elementary Divisors of Graphs and Matroids
Discrete Jordan Curve Theorems
A New Counting Formula and its Application to Edge Reconstruction
n-Graphs
Star Chromatic Number
The Solution to an Extremal Problem on Balanced Extensions of Graphs
Strongly Balanced Graphs and Random Graphs
Balanced Extensions of Graphs and Hypergraphs
Locally Homogeneous Graphs from Groups

Discrete Geometry

Symmetry in Sphere-Based Assembly Configuration Spaces
Arithmetic and Fourier Transform for the PYXIS Multi-Resolution Digital Earth Model
Computing the Discrete Fourier Transform of a Hexagonal Lattice
A Simplex Contained in a Sphere

Discrete Lines and Wandering Paths
Indexing the Aperture 3 Hexagonal Discrete Global Grid
Indexing a Discrete Global Grid
A Rearrangement Inequality and the Permutahedron

Discrete Algorithms

A Framework for the Greedy Algorithm
The Greedy Algorithm and Coxeter Matroids
Scheduling Periodic Events

Monthly Proplems

Almost Fixed Sets – Monthly Problem 10843
Super Regular Graphs – Monthly Problem 6617
Modular Power Series – Monthly Problem 10314
Scrambling Points on the Unit Circle – Monthly Problem 6647
Monthly Problem E3139