### History

### 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 PoincarĂ© Conjecture

Regular Combinatorial Maps

Combinatorial Maps

Period of a Linear Recurrence

### Tiling

Tilings from Graph Directed Iterated Function Systems

Self-Similar Polygonal Tiling

Fractal Tiling from 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 k-connected graph

A Lower Bound on the Average Size of a Connected Vertex Set of a Graph

The Average Size of a Connected Vertex Set of a Graph – Explicit Formulas and Open Problems

Contractive Digraphs and Splicing Machines

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